Least common multiple (LCM) calculator

Result

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How it works

Breaking each number into its prime factors makes the LCM easy to build: take every prime that appears in any number, at its highest power across all of them, and multiply those together. This generalizes cleanly to any number of inputs, not just two.

For two numbers, there is also a shortcut using the greatest common factor (GCF): LCM(a, b) = a × b ÷ GCF(a, b) — shown here as a useful by-product, not the main method used for three or more numbers.

Formulas used

LCM from prime factorization

LCM = product of the highest power of each prime factor present

Worked examples

Three numbers

LCM(4, 6, 10) = 60 — the smallest number that 4, 6 and 10 all divide into evenly.

Two coprime numbers

LCM(7, 9) = 63, since 7 and 9 share no common factors — their LCM is simply their product.

Assumptions and limits

Only positive whole numbers are considered — decimals are rounded and signs are ignored.
Zero is excluded, since every number is technically a factor of zero, making the LCM undefined in the usual sense.

Frequently asked questions

What is the LCM used for?

It is most commonly needed to add or subtract fractions with different denominators — the LCM of the denominators becomes the common denominator.

What is the LCM of two numbers that share no factors?

It is simply their product — with nothing in common to avoid double-counting, the smallest shared multiple is just multiplying them together.

Does the order of the numbers matter?

No — the LCM is the same no matter what order the numbers are entered in.

How is this different from the GCF?

The GCF (greatest common factor) is the largest number that divides evenly into all of them; the LCM is the smallest number they all divide evenly into — opposite ends of the same factorization.

Updated 2026-08-31

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