Least Common Multiple (LCM) Calculator
Calculate the least common multiple (LCM) of 2 to 10 positive integers: the smallest number that is a multiple of all of them at once.
How is it calculated?
The LCM of two numbers is calculated from their greatest common divisor (GCD): lcm(a,b) = (a × b) ÷ gcd(a,b). For more than two numbers, the same calculation is chained: first the LCM of the first two, then the LCM of that result with the third, and so on.
Examples
LCM of 4 and 6
The LCM of 4 and 6 is 12.
LCM of 3, 4 and 5
The LCM of 3, 4 and 5 is 60.
How to calculate it by hand, step by step
Break each number into prime factors and multiply each prime factor raised to its highest exponent.
Example with 12 and 18: 12 = 2² × 3, and 18 = 2 × 3². The LCM takes each prime factor raised to the highest exponent it appears with: 2² × 3² = 4 × 9 = 36.
This method (prime factorization) is the one usually taught in school; the one this calculator uses (via the Euclidean GCD) always gives the same result and is the one calculators and software use because it runs faster.