# Definition:Common Multiple

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## 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 $S$.

This article is complete as far as it goes, but it could do with expansion.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 $\paren {x - 2}$You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Expand}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**common multiple**