Factors & Multiples

A factor of a number divides into it exactly, with no remainder. A multiple is what you get when you multiply a number by $1, 2, 3, \dots$

Factors of $12$: the numbers that divide $12$ exactly are $1, 2, 3, 4, 6, 12$. They come in pairs that multiply to $12$: $1\times12,\ 2\times6,\ 3\times4$.

Multiples of $4$: $4, 8, 12, 16, 20, \dots$ — the four-times table, going on forever.

A number that is a multiple of both $3$ and $4$ is called a common multiple. The smallest one, $12$, is the lowest common multiple. You can find it by listing: multiples of $3$ are $3, 6, 9, 12, \dots$ and of $4$ are $4, 8, 12, \dots$ — they first meet at $12$.