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.

Can I find GCD of more than two numbers?

Yes. GCD of multiple numbers is found by computing GCD pairwise: GCD(a,b,c) = GCD(GCD(a,b), c). The tool handles up to 10 numbers at once.

What is LCM used for practically?

LCM is used in adding fractions (finding common denominators), scheduling recurring events (when do two cycles align?), and synchronising processes with different frequencies.

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.

Runs entirely in your browser — your input is never uploaded, stored, or logged.

Enter two or more numbers to find their GCD and LCM with full working shown. For prime factorisation of the same numbers, use the Prime Number Checker.