How to find the least common multiple
Three practical methods, and a worked example using 12 and 18.
By the ClearLCM team · Updated November 3, 2026
What the answer means
A multiple of 12 is a number reached by multiplying 12 by a whole number. Positive multiples include 12, 24, 36 and 48. Positive multiples of 18 include 18, 36 and 54. The first shared value is 36, so LCM(12, 18) = 36. It is the smallest positive number divisible by both inputs. This is why a common multiple is useful when matching denominators or repeated cycles.
Use the greatest common factor
The calculator uses the identity LCM(a, b) = |a × b| ÷ GCF(a, b) for nonzero integers. The GCF of 12 and 18 is 6. Divide 12 by 6 first to get 2, then multiply by 18 to obtain 36. Dividing before multiplying keeps the intermediate value smaller. The GCF is found by Euclid’s algorithm, which repeatedly replaces a pair with the smaller value and the remainder.
Choose a method you can explain
Listing multiples is easy for small values but becomes slow for large ones. Prime factorization is useful when you want to show the prime powers involved: 12 = 2² × 3 and 18 = 2 × 3², so take the larger exponent for each prime to get 2² × 3² = 36. The GCF method is efficient for a calculator. All three methods give the same answer when applied correctly.
Put the example into practice with the free least common multiple calculator.