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

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


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

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

If you already have &nbsp; ''gcd'' &nbsp; for [[greatest common divisor]], &nbsp; then this formula calculates &nbsp; ''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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