Least common multiple

The least common multiple (LCM) of two integers a and b is the smallest positive integer that is a multiple of both a and b. If there is no such positive integer, i.e. if either a or b is zero, then then LCM(a,b) is defined to be zero.

In case not both a and b are zero, the least common multiple can be computed by using the greatest common divisor (or GCD) of a and b,

	a b
LCM(a, b) =
	GCD(a, b)

Thus, Euclid's algorithm for GCD gives us a fast algorithm for LCM. As an example, the LCM of 12 and 15 is 12 * 15 / 3 = 60.