Definition
Least common multiple
The least common multiple is the smallest positive whole number that is a multiple of every given positive whole number.
What it means
List the positive multiples of each number and watch for the first number that appears in every list. That first meeting point is the least common multiple. It is useful when repeating cycles need to meet or fractions need a shared denominator.
Remember it
Follow the multiple lists until they meet for the first time.
Example
Multiples of 8 begin 8, 16, 24, 32. Multiples of 12 begin 12, 24, 36. The first shared number is 24, so the least common multiple is 24.
Watch for
48 is a common multiple of 8 and 12, but it is not the least one because 24 comes first.
Common mix-up
A least common multiple is made by multiplying; it is usually at least as large as the greatest given number.
Exact meaning
For two or more positive whole numbers, the least common multiple is the smallest positive whole number that each given number divides exactly. In UK usage, it is also called the lowest common multiple.