multiple

When you skip-count by a number — 3, 6, 9, 12, and onward — every place you land is a multiple of that number. A multiple is simply what you get by multiplying a given integer by some other integer, the mirror image of divisibility seen from the other side.

Precisely, an integer m is a multiple of an integer a if there is an integer k with m = a times k. So the multiples of 3 are ..., −6, −3, 0, 3, 6, 9, ..., extending in both directions and always including 0, since 0 = a times 0 for every a. Saying m is a multiple of a is exactly the same statement as saying a divides m.

Multiples are the natural setting for the least common multiple, the smallest positive number that appears in two different multiplication tables at once — indispensable when adding fractions with unlike denominators. A small caution: 0 is a multiple of every integer, but 0 is a multiple of nothing else useful, and outside the integers the term loses its clean meaning, since you could reach any number by multiplying.