\begin{definition}[Definition:Common Multiple]
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 $S$.
{{expand|Expand the concept to general algebraic expressions, for example that $\paren {2 x + 1} \paren {x - 2}$ is a '''common multiple''' of $\paren {2 x + 1}$ and $\paren {x - 2}$}}
\end{definition}