LCM and GCD Calculator

About this calculator

The greatest common divisor (GCD) of two integers is the largest number that divides both evenly, typically found via the Euclidean algorithm (repeated division with remainder — one of the oldest algorithms in mathematics, dating to Euclid's Elements). The least common multiple (LCM) is the smallest number both integers divide into evenly, computed from the GCD via LCM(a,b) = (a×b) / GCD(a,b).

These concepts are everywhere: students use GCD to simplify fractions to lowest terms; the Euclidean algorithm underlies key steps in RSA cryptography (computing modular inverses); and LCM solves scheduling problems like finding when two repeating events next coincide (e.g. buses on different cycles, or gear ratios in mechanical design). Enter two integers to get both the GCD and LCM.