Quick start
- Type two or more whole numbers separated by commas or spaces, for example 24, 36, 60.
- Read each prime factorization.
- See the GCF and LCM built from those primes, with Euclid's algorithm as a check.
GCF vs LCM in plain words
The greatest common factor is the biggest number that divides into all of them. The least common multiple is the smallest number they all divide into. The GCF is never larger than your smallest number; the LCM is never smaller than your largest.
Example: 24, 36 and 60
24 = 2³ × 3, 36 = 2² × 3² and 60 = 2² × 3 × 5. For the GCF, take only the primes all three share, at the lowest power: 2² × 3 = 12. For the LCM, take every prime that appears, at its highest power: 2³ × 3² × 5 = 360.
A shortcut for two numbers
For any two numbers a and b, GCF × LCM = a × b. So once you know the GCF of 24 and 36 is 12, the LCM is 24 × 36 ÷ 12 = 72.
Where you will use them
- LCM: finding a common denominator, or when two repeating events line up again.
- GCF: simplifying fractions, or splitting things into equal groups with nothing left over.
Common questions
Are GCF, GCD and HCF the same?
Yes. They are three names for the greatest common factor.
What if the numbers have no common factor?
The GCF is 1, the numbers are called coprime, and the LCM is their product.
How many numbers can I enter?
As many as you like.