GCD and LCM
Greatest common divisor · least common multiple
The GCD is the largest number dividing all of the inputs, the LCM — the smallest divisible by all of them. Relationship: GCD(a,b)·LCM(a,b) = a·b.
The GCD (greatest common divisor) is the largest number that divides all of the inputs with no remainder, and the LCM (least common multiple) — the smallest number divisible by each of them.
The GCD is found quickly with the Euclidean algorithm, and the LCM from the relationship:
The calculator accepts any number of values and also shows their prime factorization — because the GCD is the product of common factors, while the LCM covers all factors raised to their highest powers.
Examples
Frequently asked questions
What is the LCM used for?+
Mainly for adding fractions (a common denominator) and for "how often will two cyclic events coincide" problems — e.g. buses leaving every 12 and 18 minutes coincide every LCM = 36 minutes.
How is the GCD related to the LCM?+
The product of the GCD and LCM of two numbers equals the product of those numbers: GCD(a,b)·LCM(a,b) = a·b. Knowing one, you can easily find the other.
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