RosettaCodeData/Task/Least-common-multiple/00DESCRIPTION

;Task:
Compute the least common multiple of two integers.

Given   ''m''   and   ''n'',   the least common multiple is the smallest positive integer that has both   ''m''   and   ''n''   as factors.


;Example:
The least common multiple of 12 and 18 is 36, because 12 is a factor (12 × 3 = 36), and 18 is a factor (18 × 2 = 36), and there is no positive integer less than 36 that has both factors.   As a special case, if either   ''m''   or   ''n''   is zero, then the least common multiple is zero.

One way to calculate the least common multiple is to iterate all the multiples of   ''m'',   until you find one that is also a multiple of   ''n''.

If you already have   ''gcd''   for [[greatest common divisor]],   then this formula calculates   ''lcm''.

<big>
:::: <math>\operatorname{lcm}(m, n) = \frac{|m \times n|}{\operatorname{gcd}(m, n)}</math>
</big>

One can also find &nbsp; ''lcm'' &nbsp; by merging the [[prime decomposition]]s of both &nbsp; ''m'' &nbsp; and &nbsp; ''n''.


;See also:
* &nbsp; MathWorld entry: &nbsp; [http://mathworld.wolfram.com/LeastCommonMultiple.html Least Common Multiple].
* &nbsp; Wikipedia entry: &nbsp; [[wp:Least common multiple|Least common multiple]].
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