# Definition:Common Multiple

## Definition

Let $S$ be a finite set of non-zero integers, that is:

$S = \set {x_1, x_2, \ldots, x_n: \forall k \in \N^*_n: x_k \in \Z, x_k \ne 0}$

Let $m \in \Z$ such that all the elements of $S$ divide $m$, that is:

$\forall x \in S: x \divides m$

Then $m$ is a common multiple of all the elements in $S$.