LCM & GCF Calculator

What the LCM and GCF mean

The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest whole number that divides every number in a list without a remainder. The GCF of 12, 18 and 30 is 6. The least common multiple (LCM) is the smallest positive number that is a multiple of every number in the list. The LCM of 12, 18 and 30 is 180. Together they are the foundation of fraction arithmetic, ratio simplification and many scheduling puzzles.

This calculator accepts as many numbers as you like and uses big-integer arithmetic, so even very large inputs return exact answers. It also lists the prime factorization of each number, which is the classic school method for finding both values by hand.

How to find them by hand

With prime factorization, write each number as a product of primes. The GCF multiplies the primes shared by all numbers, using the smallest exponent. The LCM multiplies every prime that appears in any number, using the largest exponent. For 12 = 2² × 3, 18 = 2 × 3² and 30 = 2 × 3 × 5, the GCF is 2 × 3 = 6 and the LCM is 2² × 3² × 5 = 180. The Euclidean algorithm is faster for big numbers: GCF(48, 18) → 48 mod 18 = 12 → 18 mod 12 = 6 → 12 mod 6 = 0, so the GCF is 6.

Where you will use them

Use the GCF to reduce a fraction to lowest terms, split items into the largest equal groups, or tile a floor with the biggest square tiles. Use the LCM to find a common denominator when adding fractions, or to work out when repeating events line up, for example buses arriving every 12 and 18 minutes meet again after 36 minutes. A handy relationship for two numbers is GCF × LCM = a × b. Everything is calculated locally in your browser, so nothing you type is uploaded or stored.