GCD (Greatest Common Divisor) is the largest number that divides all given numbers. Also called HCF (Highest Common Factor).

LCM (Least Common Multiple) is the smallest number that all given numbers divide into evenly.

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LCM & GCD Calculator

Find the Least Common Multiple and Greatest Common Divisor.

Enter Numbers (comma separated)

GCD (Greatest Common Divisor)

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Also called HCF

LCM (Least Common Multiple)

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Formulas

GCD Relationship

LCM(a,b) × GCD(a,b) = a × b

Finding LCM

LCM(a,b) = (a × b) / GCD(a,b)

GCD uses Euclidean algorithm: repeatedly divide larger by smaller, GCD is last non-zero remainder.

LCM(a,b) = (a × b) ÷ GCD(a,b). This relationship makes LCM easy once GCD is known.

For 3+ numbers, calculate GCD/LCM pairwise. GCD(a,b,c) = GCD(GCD(a,b), c) and same for LCM.

LCM × GCD = Product of the numbers. This is a useful verification check.

Enter comma-separated positive integers. At least 2 numbers required for calculation.

Find LCM of denominators to get common denominator. 1/4 + 1/6 = 3/12 + 2/12 (LCM of 4,6 is 12).

Divide numerator and denominator by GCD to reduce fractions. 24/36 ÷ GCD(12) = 2/3.

Find when events sync up. If buses run every 12 and 18 minutes, they sync every LCM(12,18)=36 minutes.

When do runners meet again? Use LCM of lap times to find when they return to start together.

Find smallest square that can be tiled by rectangles of different sizes. Use LCM of dimensions.

GCD and LCM are used in algorithms for cryptography, timing, and resource allocation.