The lowest common multiple of two integers is the smallest positive integer that both numbers are factors of. In other words, it is the smallest positive integer that is a multiple of both numbers. We can similarly find the lowest common multiple of more than two numbers.

For example, to find the lowest common multiple of \(12\) and \(18\), we start by writing down lists of numbers, in increasing order, that are multiples of each number. The lowest common multiple is the smallest number that occurs in both lists. So, the lowest common multiple of \(12\) and \(18\) is \(36\).

Note that \(72\) is also a common multiple of \(12\) and \(18\), but it is not the lowest common multiple, because \(36\) is a common multiple that is smaller.

Note: Before we start writing down multiples of \(12\) and \(18\), we know that these numbers have one common multiple: \(12 \times 18 = 216\), so we know our lists of common multiples will eventually stop.

Another term for "lowest common multiple" is "least common multiple".