How lcm calculator works
The least common multiple (LCM) is the smallest positive integer that is divisible by all the given numbers. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.
This calculator finds the LCM using the relationship between GCD and LCM: LCM(a, b) = (a times b) / GCD(a, b). For multiple numbers, it reduces them pairwise. This is efficient and works for any set of positive integers.
The LCM is useful for finding common denominators when adding fractions, scheduling repeating events, and solving number theory problems. Enter two or more comma-separated integers.
Frequently asked questions
What is the LCM?
The least common multiple (LCM) is the smallest positive integer divisible by all given numbers. For example, LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6.
How is the LCM calculated?
The calculator uses the formula LCM(a, b) = (a times b) / GCD(a, b), where GCD is the greatest common divisor. For more than two numbers, it reduces them pairwise.
How is LCM different from GCD?
GCD finds the largest number that divides all inputs. LCM finds the smallest number that all inputs divide into. GCD(4,6)=2, while LCM(4,6)=12.
What is LCM used for?
LCM is used to find common denominators when adding fractions, to schedule repeating events, and in number theory. For example, to add 1/4 + 1/6, you find LCM(4,6)=12 as the common denominator.