GCF & LCM Calculator

GCF is the largest number that divides evenly into all of yours — the biggest equal groups you can split things into. LCM is the smallest number all of yours divide into — the first time repeating cycles line up. Concretely: GCF(12, 18) = 6 reduces 12/18 to 2/3; LCM(4, 6) = 12 means two events every 4 and 6 days coincide every 12.

Yes — greatest common divisor (GCD), highest common factor (HCF), and greatest common factor (GCF) are one concept with regional naming: GCF dominates US classrooms, HCF is common in UK and Indian curricula, GCD in higher math and programming. Any teacher accepts any of them.

Break each number into primes — 12 = 2² × 3, 18 = 2 × 3². For GCF, take each prime appearing in all numbers at its lowest power: 2 × 3 = 6. For LCM, take every prime that appears anywhere at its highest power: 2² × 3² = 36. The calculator displays exactly this so you can copy the method onto homework.

For exactly two numbers, always — GCF(a,b) × LCM(a,b) = a × b, shown as a check whenever you enter two. With three or more numbers the identity breaks down, which is a classic trick-question fact: GCF(2,4,6) × LCM(2,4,6) = 2 × 12 = 24, but 2 × 4 × 6 = 48.