<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- -->
<!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" >
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head><title>lcm -- least common multiple</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_lcm_lp__Monomial__Ideal_rp.html">next</a> | <a href="_koszul_lp__Z__Z_cm__Matrix_rp.html">previous</a> | <a href="_lcm_lp__Monomial__Ideal_rp.html">forward</a> | <a href="_koszul_lp__Z__Z_cm__Matrix_rp.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div>
</td>
</tr>
</table>
<hr/>
<div><h1>lcm -- least common multiple</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>lcm(x,y,...)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>x</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, all the elements should be integers, rational numbers or ring elements</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>m</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, the least common multiple of the elements x,y,...</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : lcm(-6,15,14)
o1 = 210</pre>
</td></tr>
<tr><td><pre>i2 : lcm(-6/7,15,14)
o2 = 210
o2 : QQ</pre>
</td></tr>
<tr><td><pre>i3 : R = QQ[a..d];</pre>
</td></tr>
<tr><td><pre>i4 : lcm(a^2-d^2,(a-d)*(b+c))
2 2 2 2
o4 = a b + a c - b*d - c*d
o4 : R</pre>
</td></tr>
<tr><td><pre>i5 : factor oo
o5 = (b + c)(- a + d)(a + d)(-1)
o5 : Expression of class Product</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_gcd.html" title="greatest common divisor">gcd</a> -- greatest common divisor</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>lcm</tt> :</h2>
<ul><li>lcm(List)</li>
<li>lcm(QQ,QQ)</li>
<li>lcm(QQ,ZZ)</li>
<li>lcm(RingElement,RingElement)</li>
<li>lcm(RingElement,ZZ)</li>
<li>lcm(Sequence)</li>
<li>lcm(ZZ,QQ)</li>
<li>lcm(ZZ,RingElement)</li>
<li>lcm(ZZ,ZZ)</li>
<li><span><a href="_lcm_lp__Monomial__Ideal_rp.html" title="least common multiple of all minimal generators">lcm(MonomialIdeal)</a> -- least common multiple of all minimal generators</span></li>
</ul>
</div>
</div>
</body>
</html>
