What is the greatest common divisor (GCD)?

The GCD is the largest number that divides two or more numbers without a remainder. For 12 and 18, the GCD is 6 because it is the largest number dividing both evenly.

What is the least common multiple (LCM)?

The LCM is the smallest positive number that is a multiple of two or more numbers. For 4 and 6, the LCM is 12 because 12 is the smallest number divisible by both.

How do I find the GCD?

Use the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is zero. The last nonzero remainder is the GCD.

How do I find the LCM?

Divide the product of the two numbers by their GCD. For 4 and 6, (4 × 6) / 2 = 12. This relationship works for any pair and is the fastest method.

Why are LCM and GCD useful?

The GCD simplifies fractions and ratios. The LCM is used to find common denominators when adding fractions, to schedule repeating events, and in many number theory applications.

LCM & GCD Calculator

Compute the LCM and GCD of any set of numbers. Enter two or more integers and this calculator returns their greatest common divisor and least common multiple, with the working method shown.

Numbers (comma separated)