How this calculator works
The GCF is the largest number that divides all of them. It uses the prime factors they share, each at its lowest power.
The LCM is the smallest number all of them divide into. It uses every prime that appears, each at its highest power.
For two numbers, GCF × LCM = the product of the numbers.
The calculator uses the Euclidean algorithm, which is fast even for large numbers.
Worked example
12, 18 and 30
- 12 = 2 × 2 × 3, 18 = 2 × 3 × 3, 30 = 2 × 3 × 5.
- Shared primes: 2 and 3, so GCF = 6.
- Highest powers: 2², 3², 5, so LCM = 4 × 9 × 5 = 180.
Questions people ask
What is GCF used for?
Simplifying fractions and ratios, and splitting things into the largest equal groups.
What is LCM used for?
Finding common denominators when adding fractions, and working out when repeating events line up.
Is GCF the same as GCD or HCF?
Yes. Greatest common factor, greatest common divisor and highest common factor are the same thing.
What is the Euclidean algorithm?
Repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is 0. For 48 and 18: 48 mod 18 = 12, 18 mod 12 = 6, 12 mod 6 = 0, so the GCF is 6.
Last reviewed October 2, 2026