Least Common Multiple (LCM) Calculator

Find the LCM of a set of numbers. This tool also shows the work using 6 different methods.

The Least Common Multiple (LCM) is:

Step-by-Step Methods

What is the Least Common Multiple (LCM)?

The Least Common Multiple (LCM), also known as the Lowest Common Multiple (LCM) or Least Common Divisor (LCD), is the smallest positive integer that is evenly divisible by all the numbers in a given set.

For example, for $LCM(a,b)$, it is the smallest number $k$ such that $k/a$ and $k/b$ are both integers. $LCM(2,3) = 6$ because 6 is the smallest number divisible by both 2 and 3.

Properties of LCM

  • Commutative: $LCM(a, b) = LCM(b, a)$
  • Associative: $LCM(a, b, c) = LCM(LCM(a, b), c)$
  • Relationship with GCF: $LCM(a,b) \times GCF(a,b) = a \times b$