-
Notifications
You must be signed in to change notification settings - Fork 1
Expand file tree
/
Copy pathlcm.html
More file actions
431 lines (358 loc) · 39.1 KB
/
lcm.html
File metadata and controls
431 lines (358 loc) · 39.1 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
<!doctype html>
<html class="cpprefjp" lang="ja" itemscope="" itemtype="http://schema.org/WebPage">
<head>
<!-- Google tag (gtag.js) -->
<script async src="https://www.googletagmanager.com/gtag/js?id=G-NXNBNVBTJS"></script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments);}
gtag('js', new Date());
gtag('config', 'G-NXNBNVBTJS');
</script>
<meta charset="UTF-8">
<title>lcm - cpprefjp C++日本語リファレンス</title>
<meta name="viewport" content="width=device-width,initial-scale=1">
<meta name="keywords" content="
C++,標準ライブラリ,リファレンス,ドキュメント,STL,std,numeric,function template,std,cpp17
">
<meta name="title" content="lcm - cpprefjp C++日本語リファレンス" />
<meta itemprop="name" content="lcm - cpprefjp C++日本語リファレンス" />
<meta property="og:title" content="lcm - cpprefjp C++日本語リファレンス" />
<meta property="og:url" content="https://cpprefjp.github.io/reference/numeric/lcm.html" />
<meta property="og:site_name" content="cpprefjp - C++日本語リファレンス" />
<meta property="og:type" content="article" />
<meta property="og:description" content="最小公倍数 (least common multiple) を求める。" />
<meta name="twitter:card" content="summary" />
<meta name="twitter:title" content="lcm - cpprefjp C++日本語リファレンス" />
<meta name="twitter:url" content="https://cpprefjp.github.io/reference/numeric/lcm.html" />
<meta name="twitter:description" content="最小公倍数 (least common multiple) を求める。" />
<link rel="alternate" type="application/atom+xml" title="Atom" href="https://cpprefjp.github.io/rss.xml" />
<link rel="apple-touch-icon" sizes="180x180" href="../../static/favicons/apple-touch-icon.png?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95">
<link rel="icon" type="image/png" sizes="32x32" href="../../static/favicons/favicon-32x32.png?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95">
<link rel="icon" type="image/png" sizes="16x16" href="../../static/favicons/favicon-16x16.png?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95">
<link rel="manifest" href="../../manifest.json?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95">
<meta name="theme-color" content="#f5f8fc">
<link rel="stylesheet" href="../../static/pygments/default.css?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95">
<!-- <link rel="stylesheet" href="../../static/css/root.css"> -->
<script>
window.MathJax = {
tex: {
inlineMath: [ ['$','$'] ],
displayMath: [ ['$$','$$'] ],
processEscapes: true
},
chtml: {
displayAlign: 'left',
displayIndent: '2.0em',
},
};
</script>
<!-- IEはサポートしないので https://polyfill.io/v3/polyfill.min.js?features=es6 は読み込まない -->
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<link href="../../static/kunai/css/kunai-stage-0.css?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95" rel="stylesheet">
<link href="../../static/kunai/css/kunai-stage-1.css?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95" rel="stylesheet">
<link href="../../static/kunai/css/kunai-stage-2.css?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95" rel="stylesheet">
<link href="../../static/kunai/css/kunai-stage-3.css?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95" rel="stylesheet">
<script type="text/javascript" src="../../static/kunai/js/kunai-vendor.js?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95"></script>
<script type="text/javascript" src="../../static/kunai/js/kunai.js?cachebust=be86fa2321ebe02b6955b61b98b778e377bcbf95"></script>
<script type="text/javascript">
document.addEventListener('DOMContentLoaded', function() {
var kn = new Kunai;
kn.cpprefjp();
});
</script>
</head>
<body>
<header data-kunai-mdinfo="{"meta": {"header": ["numeric"], "id-type": ["function template"], "namespace": ["std"], "cpp": ["cpp17"]}, "sources": [{"id": "1100bc591a15f17af7f7152a6560a72bf7387cdf", "source": "#include <cassert>\n#include <numeric>\n\nint main() {\n assert(std::lcm(3, 4) == 12);\n assert(std::lcm(4, 3) == 12);\n\n // \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u6700\u5c0f\u516c\u500d\u6570\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u308b\n static_assert(std::lcm(0, 1) == 0);\n static_assert(std::lcm(4u, -6l) == 12);\n}\n"}, {"id": "6c87cc8a65a42b07f588f900affb8f602ec6d9ec", "source": "#include <iostream>\n#include <cstdint>\n#include <numeric>\n\nint main() {\n std::uint16_t m = 20000;\n std::uint16_t n = 40000;\n\n // \u6a19\u6e96std::lcm()\u306e\u52d5\u4f5c\u306f\u5b9f\u88c5\u5b9a\u7fa9\n std::cout << \"std::lcm(\" << m << \", \" << n << \") \" << std::lcm(m, n) << std::endl;\n\n // \u516c\u5f0f\u901a\u308a\u306e\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u3057\u3084\u3059\u3044\u6700\u5c0f\u516c\u500d\u6570\u306e\u5b9f\u88c5\n volatile std::uint16_t t = m * n; // \u6700\u9069\u5316\u56de\u907f\u306e\u305f\u3081\u306e\u5909\u6570\n std::cout << \"formal lcm(\" << m << \", \" << n << \") \" << (t / std::gcd(m, n)) << std::endl;\n\n // \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u3057\u306b\u304f\u3044\u3088\u3046\u516c\u5f0f\u3092\u6539\u826f\u3057\u305f\u5b9f\u88c5\n auto g = std::gcd(m, n);\n std::cout << \"improved lcm(\" << m << \", \" << n << \") \" << m * (n / g) << std::endl;\n}\n"}, {"id": "9a92c3b5bb6dc2b98397cebc595543e261b68a1f", "source": "#include <cassert>\n#include <numeric>\n#include <vector>\n\n// \u53ef\u5909\u5f15\u6570\u3067\u6700\u5c0f\u516c\u500d\u6570\u3092\u6c42\u3081\u308b\u95a2\u6570\ntemplate <class T>\nT vlcm(T m, T n) {\n return std::lcm(m, n);\n}\n\ntemplate <class T, class... Args>\nT vlcm(T a, Args... args) {\n return vlcm(a, vlcm(args...));\n}\n\nint main() {\n // 2\u3064\u305a\u3064\u6700\u5c0f\u516c\u500d\u6570\u3092\u6c42\u3081\u308b\n assert(std::lcm(std::lcm(3, 4), 6) == 12);\n\n // \u30ea\u30b9\u30c8\u5168\u4f53\u306e\u6700\u5c0f\u516c\u500d\u6570\u3092\u6c42\u3081\u308b\n std::vector<int> v = {3, 4, 6};\n int r = std::accumulate(v.begin(), v.end(), 1, [](int m, int n) {\n return std::lcm(m, n);\n });\n assert(r == 12);\n\n // \u53ef\u5909\u5f15\u6570\u3067\u6700\u5c0f\u516c\u500d\u6570\u3092\u6c42\u3081\u308b\n assert(vlcm(3, 4, 6) == 12);\n}\n"}], "page_id": ["reference", "numeric", "lcm"]}">
<nav class="navbar navbar-default" role="navigation">
<div class="container-fluid">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar-collapse">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="../../index.html">
<div class="title-wrapper clearfix">
<div class="title">cpprefjp - C++日本語リファレンス</div>
</div>
</a>
</div>
<div class="collapse navbar-collapse" id="navbar-collapse">
<ul class="nav navbar-nav navbar-right">
<li>
<div class="google-search">
<script>
(function() {
var cx = '013316413321391058734:ji_u66hl7hq';
var gcse = document.createElement('script');
gcse.type = 'text/javascript';
gcse.async = true;
gcse.src = (document.location.protocol == 'https:' ? 'https:' : 'http:') +
'//www.google.com/cse/cse.js?cx=' + cx;
var s = document.getElementsByTagName('script')[0];
s.parentNode.insertBefore(gcse, s);
})();
</script>
<div class="gcse-search"></div>
</div>
</li>
<li>
<a href="https://github.com/cpprefjp/site">GitHub Project</a>
</li>
</ul>
</div>
</div>
</nav>
</header>
<main id="main" role="main">
<div class="container-fluid">
<div class="row">
<div class="col-sm-9 col-sm-push-3" itemscope itemtype="http://schema.org/Article">
<div class="row">
<div class="col-sm-12 google-search-result">
<gcse:searchresults></gcse:searchresults>
</div>
</div>
<div class="row">
<div class="col-sm-12 content-header">
<ol class="breadcrumb">
<li itemscope itemtype="http://www.schema.org/SiteNavigationElement">
<span>
<a href="../../index.html" itemprop="url">
<i class="fa fa-fw fa-home"></i>
</a>
</span>
</li>
<li itemscope itemtype="http://www.schema.org/SiteNavigationElement">
<span>
<a href="../../reference.html" itemprop="url">
<span itemprop="name">リファレンス</span>
</a>
</span>
</li>
<li itemscope itemtype="http://www.schema.org/SiteNavigationElement">
<span>
<a href="../../reference/numeric.html" itemprop="url">
<span itemprop="name">numeric</span>
</a>
</span>
</li>
<li class="active" itemscope itemtype="http://www.schema.org/SiteNavigationElement">
<span>
<span itemprop="name">lcm</span>
</span>
</li>
</ol>
<div class="crsearch"></div>
</div>
</div>
<div class="row">
<div class="col-sm-12 edit-button">
<p class="text-right"><small>
最終更新日時(UTC):
<span itemprop="datePublished" content="2025-07-11T17:16:44">
2025年07月11日 17時16分44秒
</span>
<br/>
<span itemprop="author" itemscope itemtype="http://schema.org/Person">
<span itemprop="name">Koichi Murase</span>
</span>
が更新
</small></p>
<p class="text-right">
<a class="history" target="_blank" href="https://github.com/cpprefjp/site/commits/master/reference/numeric/lcm.md">
<span class="fa fa-fw fa-clock-o fa-flip-horizontal"></span>履歴
</a>
<a class="edit" target="_blank" href="https://github.com/cpprefjp/site/edit/master/reference/numeric/lcm.md">
<span class="fa fa-fw fa-pencil"></span>編集
</a>
</p>
</div>
</div>
<div class="row">
<div class="col-sm-12 content-body">
<div class="identifier-type">function template</div><div class="header"><numeric></div><h1 itemprop="name"><span class="namespace" title="namespace std">std::</span><span class="token">lcm</span><span class="cpp cpp17" title="C++17で追加">(C++17)</span></h1>
<div itemprop="articleBody"><p><div class="codehilite"><pre><span></span><code><span class="k">namespace</span><span class="w"> </span><span class="nn">std</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">M</span><span class="p">,</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">N</span><span class="o">></span>
<span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="n"><a href="../type_traits/common_type.html">common_type_t</a></span><span class="o"><</span><span class="n">M</span><span class="p">,</span><span class="w"> </span><span class="n">N</span><span class="o">></span><span class="w"> </span><span class="n">lcm</span><span class="p">(</span><span class="n">M</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
<span class="p">}</span>
</code></pre></div>
</p>
<h2>概要</h2>
<p>最小公倍数 (least common multiple) を求める。</p>
<h2><a class="cpprefjp-defined-word" data-desc="関数等の意味論を構成する要素の1つ。Mandates。満たさなければプログラムが不適格となる要件。この要件は、オーバーロード解決によって選択された関数内での`static_assert`の定数条件式や、関数に対するdelete宣言などで表現できる">適格要件</a></h2>
<ul>
<li>型<code>M</code> および <code>N</code> が <code>bool</code> 以外の整数型であること</li>
</ul>
<h2><a class="cpprefjp-defined-word" data-desc="関数等の意味論を構成する要素の1つ。Preconditions。関数呼び出し時に満たされていると関数が想定する条件。満たさなければ未定義の動作。契約属性の`[[expects]]`に相当">事前条件</a></h2>
<ul>
<li><code>|m|</code> および <code>|n|</code> が <code><a href="../type_traits/common_type.html">common_type_t</a><M, N></code> の値として表現できること</li>
<li><code>|m|</code> と <code>|n|</code> の最小公倍数が <code><a href="../type_traits/common_type.html">common_type_t</a><M, N></code> の値として表現できること</li>
</ul>
<h2><a class="cpprefjp-defined-word" data-desc="関数呼び出し式の評価結果となるオブジェクト・値">戻り値</a></h2>
<ul>
<li><code>m</code> または <code>n</code> が 0 の場合 0 を返す</li>
<li>それ以外の場合引数 <code>|m|</code> と <code>|n|</code> の最小公倍数を返す</li>
</ul>
<h2><a class="cpprefjp-defined-word" data-desc="問題が発生したときに、現在実行位置を過去に通過・記録した位置に戻し、文脈情報を添えて紐づけられた処理(例外ハンドラー)を呼び出す仕組み。またはその事態">例外</a></h2>
<p>投げない。</p>
<h2>備考</h2>
<ul>
<li>この関数は、公式通りに <code>abs(m * n) / gcd(m, n)</code> として実装すると、<code>m * n</code>の箇所でオーバーフローしやすい。実装によっては、式を改良することでオーバーフローしにくいようになっている場合がある<ul>
<li>GCC (libstdc++), Clang (libc++), Visual C++ : オーバーフローしにくい改良版の式として<code>abs(m) / gcd(m, n) * abs(n)</code>という実装が使用されている</li>
</ul>
</li>
</ul>
<h2>例</h2>
<h3>基本的な使い方</h3>
<p><div class="yata" id="1100bc591a15f17af7f7152a6560a72bf7387cdf"><div class="codehilite"><pre><span></span><code><span class="cp">#include <a href="../cassert.html"><cassert></a></span>
<span class="cp">#include <a href="../numeric.html"><numeric></a></span>
<span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n"><a href="../cassert/assert.html">assert</a></span><span class="p">(</span><span class="n"><span style="color:#ff0000">std::lcm</span></span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">12</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../cassert/assert.html">assert</a></span><span class="p">(</span><span class="n"><span style="color:#ff0000">std::lcm</span></span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">12</span><span class="p">);</span>
<span class="w"> </span><span class="c1">// コンパイル時に最小公倍数を求めることもできる</span>
<span class="w"> </span><span class="k">static_assert</span><span class="p">(</span><span class="n"><span style="color:#ff0000">std::lcm</span></span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
<span class="w"> </span><span class="k">static_assert</span><span class="p">(</span><span class="n"><span style="color:#ff0000">std::lcm</span></span><span class="p">(</span><span class="mi">4u</span><span class="p">,</span><span class="w"> </span><span class="mi">-6l</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">12</span><span class="p">);</span>
<span class="p">}</span>
</code></pre></div>
</div></p>
<h4>出力</h4>
<p><pre><code></code></pre></p>
<h3>オーバーフローしやすい状況の例</h3>
<p><div class="yata" id="6c87cc8a65a42b07f588f900affb8f602ec6d9ec"><div class="codehilite"><pre><span></span><code><span class="cp">#include <a href="../iostream.html"><iostream></a></span>
<span class="cp">#include <a href="../cstdint.html"><cstdint></a></span>
<span class="cp">#include <a href="../numeric.html"><numeric></a></span>
<span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n"><a href="../cstdint/uint16_t.html">std::uint16_t</a></span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">20000</span><span class="p">;</span>
<span class="w"> </span><span class="n"><a href="../cstdint/uint16_t.html">std::uint16_t</a></span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">40000</span><span class="p">;</span>
<span class="w"> </span><span class="c1">// 標準<span style="color:#ff0000">std::lcm</span>()の動作は実装定義</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"<span style="color:#ff0000">std::lcm</span>("</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">", "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">") "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::lcm</span></span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="c1">// 公式通りのオーバーフローしやすい最小公倍数の実装</span>
<span class="w"> </span><span class="k">volatile</span><span class="w"> </span><span class="n"><a href="../cstdint/uint16_t.html">std::uint16_t</a></span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最適化回避のための変数</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"formal lcm("</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">", "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">") "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="p">(</span><span class="n">t</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n"><a href="gcd.html">std::gcd</a></span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">))</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="c1">// オーバーフローしにくいよう公式を改良した実装</span>
<span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><a href="gcd.html">std::gcd</a></span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"improved lcm("</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">", "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">") "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">g</span><span class="p">)</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="p">}</span>
</code></pre></div>
</div></p>
<h4>出力例</h4>
<p><pre><code>std::lcm(20000, 40000) 40000
formal lcm(20000, 40000) 0
improved lcm(20000, 40000) 40000
</code></pre></p>
<h3>3つ以上の値に対する最小公倍数を求める</h3>
<p><div class="yata" id="9a92c3b5bb6dc2b98397cebc595543e261b68a1f"><div class="codehilite"><pre><span></span><code><span class="cp">#include <a href="../cassert.html"><cassert></a></span>
<span class="cp">#include <a href="../numeric.html"><numeric></a></span>
<span class="cp">#include <a href="../vector.html"><vector></a></span>
<span class="c1">// 可変引数で最小公倍数を求める関数</span>
<span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">T</span><span class="o">></span>
<span class="n">T</span><span class="w"> </span><span class="n">vlcm</span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::lcm</span></span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
<span class="p">}</span>
<span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">T</span><span class="p">,</span><span class="w"> </span><span class="k">class</span><span class="p">...</span><span class="w"> </span><span class="n">Args</span><span class="o">></span>
<span class="n">T</span><span class="w"> </span><span class="n">vlcm</span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">Args</span><span class="p">...</span><span class="w"> </span><span class="n">args</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">vlcm</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">vlcm</span><span class="p">(</span><span class="n">args</span><span class="p">...));</span>
<span class="p">}</span>
<span class="kt">int</span><span class="w"> </span><span class="n">main</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="c1">// 2つずつ最小公倍数を求める</span>
<span class="w"> </span><span class="n"><a href="../cassert/assert.html">assert</a></span><span class="p">(</span><span class="n"><span style="color:#ff0000">std::lcm</span></span><span class="p">(</span><span class="n"><span style="color:#ff0000">std::lcm</span></span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">),</span><span class="w"> </span><span class="mi">6</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">12</span><span class="p">);</span>
<span class="w"> </span><span class="c1">// リスト全体の最小公倍数を求める</span>
<span class="w"> </span><span class="n"><a href="../vector/vector.html">std::vector</a></span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">};</span>
<span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><a href="accumulate.html">std::accumulate</a></span><span class="p">(</span><span class="n"><a href="../vector/vector/begin.html">v.begin()</a></span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../vector/vector/end.html">v.end()</a></span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="p">[](</span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::lcm</span></span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
<span class="w"> </span><span class="p">});</span>
<span class="w"> </span><span class="n"><a href="../cassert/assert.html">assert</a></span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">12</span><span class="p">);</span>
<span class="w"> </span><span class="c1">// 可変引数で最小公倍数を求める</span>
<span class="w"> </span><span class="n"><a href="../cassert/assert.html">assert</a></span><span class="p">(</span><span class="n">vlcm</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">12</span><span class="p">);</span>
<span class="p">}</span>
</code></pre></div>
</div></p>
<h4>出力</h4>
<p><pre><code></code></pre></p>
<h2>バージョン</h2>
<h3>言語</h3>
<ul>
<li>C++17</li>
</ul>
<h3>処理系</h3>
<ul>
<li><a href="../../implementation.html#clang">Clang</a>: 4.0.0 <span aria-label="検証済" role="img" title="検証済">✅</span></li>
<li><a href="../../implementation.html#gcc">GCC</a>: 7.1.0 <span aria-label="検証済" role="img" title="検証済">✅</span></li>
<li><a href="../../implementation.html#icc">ICC</a>: ??</li>
<li><a href="../../implementation.html#visual_cpp">Visual C++</a>: ??</li>
</ul>
<h3>備考</h3>
<h4>Clang (libc++)</h4>
<ul>
<li><a class="cpprefjp-defined-word" data-desc="関数等の意味論を構成する要素の1つ。Preconditions。関数呼び出し時に満たされていると関数が想定する条件。満たさなければ未定義の動作。契約属性の`[[expects]]`に相当">事前条件</a>を満たすかどうかチェックしない。</li>
<li><code><a href="http://releases.llvm.org/5.0.0/projects/libcxx/docs/DesignDocs/DebugMode.html#using-debug-mode" target="_blank">_LIBCPP_DEBUG</a></code> マクロが<code>0</code> 以上の場合、<a class="cpprefjp-defined-word" data-desc="関数等の意味論を構成する要素の1つ。Preconditions。関数呼び出し時に満たされていると関数が想定する条件。満たさなければ未定義の動作。契約属性の`[[expects]]`に相当">事前条件</a>2を満たさなければ <code><a href="../cstdlib/abort.html">abort</a></code> する。<ul>
<li>ただしバージョン 4 系では <code><a href="../limits.html"><limits></a></code> を <code><numeric></code> より先に include しなければならない。</li>
<li>それ以外の場合（デフォルト）、オーバーフローにより<a class="cpprefjp-defined-word" data-desc="関数呼び出し式の評価結果となるオブジェクト・値">戻り値</a>が不正になることがある。</li>
</ul>
</li>
</ul>
<h4>GCC (libstdc++)</h4>
<ul>
<li><a class="cpprefjp-defined-word" data-desc="関数等の意味論を構成する要素の1つ。Preconditions。関数呼び出し時に満たされていると関数が想定する条件。満たさなければ未定義の動作。契約属性の`[[expects]]`に相当">事前条件</a>を満たすかどうかチェックしない。</li>
<li><a class="cpprefjp-defined-word" data-desc="関数等の意味論を構成する要素の1つ。Preconditions。関数呼び出し時に満たされていると関数が想定する条件。満たさなければ未定義の動作。契約属性の`[[expects]]`に相当">事前条件</a>2を満たさない場合、オーバーフローにより<a class="cpprefjp-defined-word" data-desc="関数呼び出し式の評価結果となるオブジェクト・値">戻り値</a>が不正になることがある。</li>
</ul>
<h2>参照</h2>
<ul>
<li><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2014/n3845.pdf" target="_blank">WG21 N3845 Greatest Common Divisor and Least Common Multiple</a></li>
<li><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2014/n3913.pdf" target="_blank">WG21 N3913 Greatest Common Divisor and Least Common Multiple, v2</a></li>
<li><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2014/n4061.pdf" target="_blank">WG21 N4061 Greatest Common Divisor and Least Common Multiple, v3</a></li>
<li><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0295r0.pdf" target="_blank">WG21 P0295R0 Adopt Selected Library Fundamentals V2 Components for C++17</a></li>
<li><a href="https://wg21.cmeerw.net/lwg/issue2837" target="_blank">LWG Issue 2837. <code>gcd</code> and <code>lcm</code> should support a wider range of input values</a></li>
<li><a href="https://wg21.cmeerw.net/lwg/issue2759" target="_blank">LWG Issue 2759. <code>gcd</code> / <code>lcm</code> and <code>bool</code> for the WP</a></li>
</ul>
<h2>関連項目</h2>
<ul>
<li><code><a href="gcd.html">gcd</a></code></li>
</ul>
<h2>実装例</h2>
<p>$$ \mathrm{lcm}(m, n) = \frac{|mn|}{\mathrm{gcd}(m, n)} $$</p>
<p><div class="codehilite"><pre><span></span><code><span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">M</span><span class="p">,</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">N</span><span class="o">></span>
<span class="k">constexpr</span><span class="w"> </span><span class="n"><a href="../type_traits/common_type.html">std::common_type_t</a></span><span class="o"><</span><span class="n">M</span><span class="p">,</span><span class="w"> </span><span class="n">N</span><span class="o">></span><span class="w"> </span><span class="n">gcd</span><span class="p">(</span><span class="n">M</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">mm</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><a href="../cstdlib/abs.html">abs</a></span><span class="p">(</span><span class="n">m</span><span class="p">);</span>
<span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="n">nn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><a href="../cstdlib/abs.html">abs</a></span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
<span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">mm</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">nn</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mm</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">nn</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n">mm</span><span class="w"> </span><span class="o">%=</span><span class="w"> </span><span class="n">nn</span><span class="p">;</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n">nn</span><span class="w"> </span><span class="o">%=</span><span class="w"> </span><span class="n">mm</span><span class="p">;</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">mm</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">nn</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">nn</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">mm</span><span class="p">;</span>
<span class="p">}</span>
<span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">M</span><span class="p">,</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">N</span><span class="o">></span>
<span class="k">constexpr</span><span class="w"> </span><span class="n"><a href="../type_traits/common_type.html">std::common_type_t</a></span><span class="o"><</span><span class="n">M</span><span class="p">,</span><span class="w"> </span><span class="n">N</span><span class="o">></span><span class="w"> </span><span class="n">lcm</span><span class="p">(</span><span class="n">M</span><span class="w"> </span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n"><a href="../cstdlib/abs.html">abs</a></span><span class="p">(</span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">gcd</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n"><a href="../cstdlib/abs.html">abs</a></span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
<span class="p">}</span>
</code></pre></div>
</p></div>
</div>
</div>
</div>
<div id="sidebar" class="col-sm-3 col-sm-pull-9">
</div>
</div>
</div>
</main>
<footer class="footer navbar navbar-default">
<div class="container-fluid">
<p><small>
本サイトの情報は、
<a href="https://creativecommons.org/licenses/by/4.0/deed.ja" rel="nofollow">クリエイティブ・コモンズ 表示 4.0 非移植 ライセンス(CC BY)</a>
の下に提供されています。
</small></p>
</div>
</footer>
</body>
</html>