Lowest common multiple
The lowest common multiple (LCM) is the smallest number that two or more numbers share - the first multiple that they both have in common.
For example:
The lowest common multiple (LCM) of 4 and 5 is 20 because \({4}\times{5}~=~20\) and \({5}\times{4}~=~20\).
Question
What is the LCM of \({5}\) and \({8}\)?
The multiples of \({5}\) are \({5}\), \({10}\), \({15}\), \({20}\), \({25}\), \({30}\), \({35}\), \({40}\) \({...}\)
The multiples of \({8}\) are \({8}\), \({16}\), \({24}\), \({32}\), \({40}\), \({48}\), \({56}\) \({...}\)
So the LCM of \({5}\) and \({8}\) is \({40}\).
Question
What is the LCM of \({3}\) and \({6}\)?
The multiples of \({3}\) are \({3}\), \({6}\)...and you can stop there. \(6\) is a multiple of \(3\) and it is the first (or lowest) multiple of itself.
So the LCM of \(3\) and \(6\) is \(6\).
