GCF and LCM calculator

How it works

1. Type two or more whole numbers on a line, separated by spaces or commas — or a single number to factor it into primes.
2. Put each problem on its own line to work several at once.
3. The GCF and LCM appear first, then the prime factorization, the division ladder and, for two numbers, Euclid’s algorithm and a check.

Frequently asked questions

How do you find the GCF and LCM with prime factorization?

Factor each number into primes: 12 = 2² × 3 and 18 = 2 × 3². The GCF takes the primes they share, each with its smaller power: 2 × 3 = 6. The LCM takes every prime with its greater power: 2² × 3² = 36.

What is the division ladder?

The numbers are divided side by side by primes until only ones are left. The primes that divided every number (marked *) multiply to the GCF; all the primes together multiply to the LCM.

What is Euclid’s algorithm?

Divide the larger number by the smaller and keep the remainder; then divide the smaller by the remainder, and so on. The last remainder that is not zero is the GCF: 18 = 1 × 12 + 6, 12 = 2 × 6 + 0, so the GCF is 6.

Is GCF the same as HCF and GCD?

Yes: greatest common factor, highest common factor and greatest common divisor are three names for the same number.

Is anything uploaded?

No. It is worked out in your browser, and nothing you type leaves your computer.