The least common multiple of two (or more) nonzero integers is the least positive integer divisible by all of them. This is usually denoted lcm. For example, lcm(-12,30)=60. NoticeEuclidean algorithm, to find the least common multiple without factoring. However, if we know the prime factorization of a is , and that of b is , then lcm(a,b) is .
We can generalize gcd(a,b).lcm(a,b) = ab to three variables in a number of ways:
Finally, as a direct result of the properties of min and max functions we have the dual relations:
See Also: GCD