GCD and LCM Calculator

The GCD, also called the greatest common factor (GCF) or highest common factor (HCF), is the largest whole number that divides every number in the list with no remainder.

The LCM is the smallest positive whole number that every number in the list divides into evenly. It is a common multiple of all of them.

The GCD is found with the Euclidean algorithm, repeatedly taking remainders until one reaches zero. The LCM uses the identity lcm(a, b) = |a / gcd(a, b) * b|. For longer lists the calculator folds each result across the numbers two at a time.

Yes. Enter as many integers as you like. The GCD and LCM are reduced across the whole list, so the answers apply to every number at once.

The GCD reduces fractions to lowest terms and simplifies ratios. The LCM finds common denominators and solves scheduling problems, such as when two repeating events line up again.

The tool works on non-zero integers. Every number is a multiple of zero and the GCD of all zeros is undefined, while decimals do not have a well-defined GCD or LCM.