LCM Calculator
Find the least common multiple of two or three whole numbers using the GCF relationship.
How it works
lcm(a, b) = |a × b| ÷ gcd(a, b) · lcm(a, b, c) = lcm(lcm(a, b), c)
The least common multiple is the smallest positive number that every input divides into evenly. Rather than list multiples, it is fastest to use the identity lcm(a, b) = a × b ÷ gcd(a, b): dividing out the shared factors before multiplying avoids overcounting. For three numbers, chain the operation using the LCM of the first pair.
Worked example
For 4 and 6, the GCF is 2, so the LCM is 4 × 6 ÷ 2 = 24 ÷ 2 = 12. Both 4 and 6 divide into 12 (three times and twice).
Sources: Least common multiple — Wikipedia
Frequently asked questions
What is the LCM used for?
The most common use is adding or subtracting fractions with different denominators — the least common denominator is just the LCM of the denominators.
Why divide by the GCF?
Multiplying two numbers double-counts the factors they share. Dividing the product by their greatest common factor removes that overlap, giving the smallest common multiple instead of just a common one.
Can the LCM involve zero?
No. Zero is a multiple of every number, so there is no smallest positive common multiple involving 0. The LCM is defined only for non-zero numbers.
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This calculator is for educational purposes. Double-check important results before acting on them.