What is the difference between LCM and GCF?

The GCF (Greatest Common Factor) is the largest number that divides all given numbers evenly. The LCM (Least Common Multiple) is the smallest number that is a multiple of all given numbers. GCF is used to simplify fractions, while LCM is used to find common denominators.

How is the GCF calculated?

The most efficient method is the Euclidean Algorithm: repeatedly replace the larger number with the remainder when divided by the smaller number, until the remainder is zero. The last non-zero remainder is the GCF.

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📐 Math

LCM & GCF Calculator

Calculate the Least Common Multiple (LCM) and Greatest Common Factor (GCF) for two or more numbers using the Euclidean algorithm.

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LCM & GCF — The Foundation of Number Theory

Greatest Common Factor (GCF)

The GCF (also called HCF or GCD) is the largest integer that divides all given numbers without a remainder. Our calculator uses the Euclidean Algorithm — one of the oldest algorithms in mathematics — which repeatedly replaces the larger number with the remainder until reaching zero. The last non-zero remainder is the GCF.

Least Common Multiple (LCM)

The LCM is the smallest positive integer divisible by all given numbers. It is calculated from the GCF using the identity: LCM(a,b) = |a × b| / GCF(a,b). LCM is essential for adding fractions and scheduling repeating events.