What is the LCM
The LCM, or least common multiple, is the smallest positive whole number that is a multiple of every number in a list at the same time. For example, the LCM of 4 and 6 is 12: both 4 and 6 have 12 as a multiple, and no smaller number is a multiple of both.
How to calculate LCM by factorization
A traditional way to find the LCM is to break each number down into prime factors and multiply every factor involved, each raised to the highest exponent found among the numbers. This calculator uses the Euclidean algorithm internally, which reaches the same result more directly, without needing to factor, and it also works for more than two numbers at once.
LCM and GCD: how they relate
For two numbers A and B, there is a simple relationship between the LCM and the GCD: LCM(A, B) × GCD(A, B) = A × B. This property only holds exactly for pairs of numbers, and it's a quick way to check a calculation, since multiplying the two results should match the product of the original numbers. If you only need the GCD, the GCD calculator handles that for any amount of numbers.
Practical example
Two bus lines pass a stop every 12 and 18 minutes, respectively. If both just passed together, the LCM of 12 and 18, which is 36, tells you in how many minutes they'll pass together again.