\begin{definition}[Definition:Lowest Common Multiple/Integers/General Definition]
Let $S = \set {a_1, a_2, \ldots, a_n} \subseteq \Z$ such that $\ds \prod_{a \mathop \in S} a = 0$ (that is, all elements of $S$ are non-zero).
Then the '''lowest common multiple''' of $S$:
:$\map \lcm S = \lcm \set {a_1, a_2, \ldots, a_n}$
is defined as the smallest $m \in \Z_{>0}$ such that:
:$\forall x \in S: x \divides m$
where $\divides$ denotes divisibility.
\end{definition}