Computing the LCM

This LCM calculator combines inputs pairwise using the identity lcm(a, b) = a·b / gcd(a, b), with the GCD from the Euclidean algorithm. The result is exact for any integers up to JavaScript's safe-integer range.

Prime Factorization

Each input is broken into primes for display — 4 = 2², 6 = 2·3, 8 = 2³ — and the LCM takes the highest exponent of every prime involved: 2³·3 = 24. The two approaches always agree, which the calculator demonstrates side by side.

Why the LCM Matters

Common denominators, gear teeth, repeating schedules, and synchronization problems all reduce to finding an LCM. Add fractions, plan repeating events, or check divisibility — the answer is the smallest number all inputs divide evenly.