What is the difference between GCD and LCM?

GCD (Greatest Common Divisor) is the largest number that divides all inputs exactly. LCM (Least Common Multiple) is the smallest number that all inputs divide into exactly. They are related: GCD(a,b) × LCM(a,b) = a × b.

What is the Euclidean algorithm?

An efficient method for finding GCD: GCD(a,b) = GCD(b, a mod b), repeated until the remainder is 0. Attributed to Euclid (~300 BC), it remains one of the oldest known algorithms.

GCD & LCM Calculator

Calculates the Greatest Common Divisor (GCD, also called HCF) and Least Common Multiple (LCM) of two or more integers. Shows the step-by-step working using the Euclidean algorithm for GCD and the prime factorisation method. Supports up to 10 numbers at once.

Numbers (space or comma separated)

Greatest Common Divisor (GCD / HCF)

Least Common Multiple (LCM)

GCD(12, 18, 24) = 6 — the largest number that divides all inputs evenly.
LCM(12, 18, 24) = 72 — the smallest number divisible by all inputs.

Enter two or more numbers to find their GCD and LCM with full working shown.