How this calculator works
The least common multiple is the smallest number that every input divides into evenly. It is what you need to find a common denominator. The greatest common factor is the largest number that divides all inputs, used to simplify fractions and ratios.
Formula
GCF by the Euclidean algorithm. LCM(a, b) = a × b ÷ GCF(a, b); extend to more numbers one at a time.
Frequently asked questions
Is GCF the same as GCD?
Yes. Greatest common factor (GCF), greatest common divisor (GCD) and highest common factor (HCF) all mean the same thing.
What is the LCM of 12 and 18?
The LCM of 12 and 18 is 36, and their GCF is 6.
What is the difference between LCM and GCF?
The LCM is the smallest shared multiple (always the same size or larger than the inputs); the GCF is the largest shared factor (the same size or smaller).