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 $S$.

This article is complete as far as it goes, but it could do with expansion. In particular: 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

• 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $2$: Divisibility Theory in the Integers: $2.3$ The Euclidean Algorithm
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): common multiple
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): common multiple
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): common multiple
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): common multiple