The greatest common factor (also called greatest common divisor, GCD) is the largest whole number that divides every number in the list. The calculator uses the Euclidean algorithm: gcd(a, b) = gcd(b, a mod b) until the remainder is zero. The least common multiple is the smallest number that every input divides into: lcm(a, b) = a x b / gcd(a, b).
Example: 12, 18 and 30. Prime factors are 12 = 2 x 2 x 3, 18 = 2 x 3 x 3, 30 = 2 x 3 x 5. They share one 2 and one 3, so the GCF is 6. The LCM is 180.
Simplifying fractions: divide the top and bottom by their GCF. For 12/18 the GCF is 6, so the fraction reduces to 2/3. Try the fraction calculator.
Finding a common denominator when adding fractions, and finding when repeating cycles line up, for example two buses that run every 12 and 18 minutes meet again every 36 minutes.
It is 1. Such numbers are called coprime, and their LCM is simply their product.
See also: fraction calculator · prime number checker · average calculator
Related: factorial and combinations calculator.