LCM & GCD Calculator

The GCD (also called HCF — Highest Common Factor, or GCF — Greatest Common Factor) is the largest positive integer that divides all given numbers without a remainder. GCD(12, 18) = 6 because 6 is the largest number that divides both. The Euclidean algorithm is the efficient way to compute it: GCD(18, 12) = GCD(12, 6) = GCD(6, 0) = 6.

The LCM is the smallest positive integer divisible by all the given numbers. LCM(4, 6) = 12 because 12 is the smallest number both 4 and 6 divide into evenly. Relationship with GCD: LCM(a, b) = (a × b) ÷ GCD(a, b). Used in adding/subtracting fractions with different denominators.

Two numbers are coprime (relatively prime) if their GCD = 1 — they share no common factors other than 1. Example: 8 and 15 are coprime (8 = 2³; 15 = 3 × 5; no shared prime factors). Coprimality is important in cryptography (RSA key generation), modular arithmetic, and fraction simplification.

LCM finds the smallest time when two recurring events synchronise. If bus A comes every 12 minutes and bus B every 8 minutes, LCM(12, 8) = 24 — they'll both be at the stop together every 24 minutes. Also used in music (finding common rhythm cycles) and computing (memory alignment).