Common multiple

The common multiple of two or more positive integers is a multiple common to those numbers. Any finite set of positive integers have an infinite number of common multiples.

Every common multiple of a set of integers is a multiple of the least common multiple of those integers.

For example, the least common multiple of 6, 10 and 15 is 30, and the common multiples of 6, 10 and 15 are exactly equal to the multiples of 30. (As a result of poset theory, this says that in the poset of positive integers ordered by the divisor relation, least upper bounds exist for any finite set.)

See Also