LCM Calculator
Find the least common multiple of two or more numbers, with prime factorizations and the GCF
LCM of 4, 6, 10
Least common multiple
GCF (greatest common factor)
Largest number dividing all of them
Prime factorizations
- 4 = 2²
- 6 = 2 × 3
- 10 = 2 × 5
The LCM takes every prime that appears, at its highest power. The first common multiples are 60, 120, 180, …
How it works
The least common multiple is computed from the greatest common divisor: LCM(a, b) = a × b ÷ GCD(a, b), folded across all the numbers you enter. Results use exact integer arithmetic (BigInt), so large inputs do not lose precision.
LCM via GCD
LCM(a, b) = a × b ÷ GCD(a, b)
- a, b
- the numbers
- GCD
- their greatest common divisor
Worked example
- Find the LCM of 4, 6, and 10
- LCM(4, 6) = 24 ÷ 2 = 12
- LCM(12, 10) = 120 ÷ 2 = 60
LCM = 60 — the least common denominator of 1/4, 1/6, and 1/10.
Good to know
- The least common denominator when adding fractions is exactly the LCM of the denominators.
- If two numbers share no factor (GCF = 1), their LCM is simply their product.
- For the GCF side of the problem, see the Common Factor Calculator.
Related Calculators
Frequently Asked Questions
What is the least common multiple (LCM)?
The LCM of two or more numbers is the smallest positive number that all of them divide into evenly. For 4 and 6 it is 12 — the first number that appears in both times tables.
How do I find the LCM of two numbers?
The fastest way: divide the product of the numbers by their GCF. LCM(4, 6) = 4 × 6 ÷ GCF(4, 6) = 24 ÷ 2 = 12. Alternatively, take every prime factor that appears in either number at its highest power and multiply them.
How do I find the LCM of three or more numbers?
Fold the pairwise rule: find the LCM of the first two, then the LCM of that result with the third, and so on. LCM(4, 6, 10) = LCM(12, 10) = 60.
What is the difference between LCM and GCF?
The GCF is the largest number dividing all values; the LCM is the smallest number all values divide into. For any two numbers, GCF × LCM = the product of the numbers.
Where is the LCM used in real problems?
Adding fractions (the least common denominator IS the LCM of the denominators), scheduling repeating events (two buses every 12 and 18 minutes meet every 36), and gear or rotation alignment problems.