GCD and LCM Explained

GCD / HCF

The Greatest Common Divisor (also called HCF — Highest Common Factor) is the largest number that divides both integers exactly. GCD(12, 18) = 6. Used for simplifying fractions: 12/18 = (12÷6)/(18÷6) = 2/3.

LCM

The Lowest Common Multiple is the smallest number divisible by both integers. LCM(12, 18) = 36. Used for adding fractions with different denominators: 1/12 + 1/18 = 3/36 + 2/36 = 5/36.

The Relationship

LCM(a,b) = (a × b) ÷ GCD(a,b). This elegant relationship means you only need to calculate one — the other follows directly.

LCM and GCD Calculator

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