Enter two or more whole numbers. You get the LCM, the GCF, and the check that ties the two together.
4, 6, and 15 have an LCM of 60 — 60 is the smallest number every one of the three divides evenly. The GCF this page reports alongside it is 1, meaning no single factor divides all three at once. That is a genuinely different statement from saying every pair is coprime: 4 and 6 share a factor of 2, and 6 and 15 share a factor of 3 — it is only across all three together that the overlap disappears. A GCF of 1 for a group says nothing about which pairs inside it might still share a factor.
Run 4, 6, and 15 through the GCF Calculator and the relationship becomes visible from the other side: GCF takes the lowest power of each shared prime, LCM takes the highest power of every prime that appears anywhere. For a pair, the two figures are linked exactly — GCF × LCM = the product of the two numbers — but that identity, as the FAQ below notes, only holds for exactly two inputs at a time.
Chaining a×b÷GCF(a,b) across a long list one pair at a time — dividing out the GCF at every step rather than multiplying everything together first — keeps the running numbers small. Multiplying a dozen large inputs together before dividing anything out risks a number far bigger than any of the intermediate LCMs actually needed, which matters once numbers get large even though it makes no difference to the final answer. That least common denominator is also exactly what the Fraction Calculator needs to add or subtract two fractions with different denominators.
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.
Both LCM and GCD fall out of the same prime factorisation — the Factor Calculator produces that factorisation, along with the full factor list and factor count, for any single number.
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.