Enter two or more whole numbers. You get the LCM, the GCF, and the check that ties the two together.
Multiplying the numbers together always gives a common multiple, but rarely the least one. For 4 and 6 the product is 24, yet 12 works and is smaller. Multiplying only gives the right answer when the numbers are coprime.
The efficient route is via the GCF: LCM(a, b) = a × b ÷ GCF(a, b). For 4 and 6 that is 24 ÷ 2 = 12. This calculator chains that pairwise for longer lists, dividing before multiplying at each step so intermediate values stay small.
Take every prime appearing in any of the numbers, at the highest power it reaches in any of them. That is the mirror image of the GCF rule, which takes shared primes at the lowest power. For 4 = 2², 6 = 2 × 3 and 15 = 3 × 5, the LCM takes 2², 3 and 5 — giving 60.
For two numbers, GCF × LCM = a × b, always. It is a genuinely useful shortcut. But it breaks for three or more — the calculator says so explicitly rather than showing a figure that looks like it should mean something.
Because the product double-counts whatever factors they share. Dividing by the GCF removes that duplication. The product only equals the LCM when the numbers are coprime, meaning their GCF is 1.
It gives the least common denominator. To add 1/4 and 1/6 you convert both to twelfths, because 12 is the LCM of 4 and 6. Using 24 instead works but leaves the answer needing simplification.
No. The LCM must be a multiple of every input, so it is at least as large as the biggest one. It equals the largest number exactly when that number is divisible by all the others — the LCM of 3 and 12 is 12.
Work pairwise: take the LCM of the first two, then the LCM of that with the third, and so on. Order does not affect the result.
The GCF Calculator gives the other half of the identity, and the Factor Calculator breaks a single number into its primes. To use the result as a common denominator, see the Fraction Calculator.