GCF and LCM Calculator
Both answers at once, with the working that separates them.
GCF and LCM Calculator
Telling Them Apart
The greatest common factor is the largest number that divides into all of your numbers. It is always less than or equal to the smallest one you entered. The lowest common multiple is the smallest number they all divide into, and it is always at least as large as the biggest one you entered.
If your answer is bigger than every input, it is an LCM. If it is smaller, it is a GCF. That single check catches most mix-ups.
Where Each One Is Used
Adding fractions needs the LCM, because that is the common denominator. Reducing a fraction needs the GCF, because that is what you divide top and bottom by. Same two numbers, opposite operations, which is exactly why they are so easy to swap by accident.
The Prime Factor Method
Break both numbers into primes. For the GCF, take each shared prime at the lowest power present; for the LCM, take every prime at the highest power. With 12 as 2 squared times 3 and 18 as 2 times 3 squared, the GCF is 2 times 3 which is 6, and the LCM is 4 times 9 which is 36.
The Shortcut Worth Remembering
For any two numbers, the GCF multiplied by the LCM equals the two numbers multiplied together. 6 times 36 is 216, and 12 times 18 is also 216. Find one and the other follows by division.