LCM and GCD Calculator
Find the Lowest Common Multiple (LCM) and Greatest Common Divisor / Highest Common Factor (GCD/HCF) of any two or three numbers, with full working shown.
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.
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