GCF and LCM Calculator - With Prime Factorisation
Greatest common factor and lowest common multiple
Two or more whole numbers, separated by commas or spaces.
Prime factorisation
| Number | Prime factors |
|---|
Where these two show up
The greatest common factor is the biggest number that divides all of yours; the lowest common multiple is the smallest number they all divide into. One shrinks things down, the other builds them up. Between them they cover simplifying fractions, adding fractions, cutting material without waste, and working out when two repeating events line up again.
Using it in three steps
- 1 Type two or more whole numbers, separated however you like.
- 2 Read the two answers side by side - the common factor on the left, the common multiple on the right.
- 3 Look at the factor table underneath if you need to show your working or check the result by hand.
Reading the prime factors
Every whole number above one is a product of primes in exactly one way, and the table shows that product. Once you have it, both answers follow by inspection: the common factor takes each shared prime to its lowest power, the common multiple takes every prime that appears to its highest. That is why 12 = 2² × 3 and 18 = 2 × 3² give 6 and 36.
A check you can do in your head
For any two numbers, the common factor times the common multiple equals the two numbers multiplied together. With 12 and 18 that is 6 × 36 = 216, and 12 × 18 = 216 as well. If a hand-worked answer fails this test, one of the two is wrong. It only holds for pairs, though - with three or more numbers the identity breaks down.