LCM Calculator (Least Common Multiple)
Enter two or more whole numbers to find the smallest number that all of them divide into. Use it to find a common denominator for fractions.
Result
4 = 2² 6 = 2 × 3 10 = 2 × 5
- Greatest common factor (GCF)
- 2
- Numbers entered
- 3
Formula
- Euclidean algorithm: gcf(a, b) = gcf(b, a mod b), until the remainder is 0
- lcm(a, b) = |a × b| ÷ gcf(a, b)
- GCF uses the lowest power of each shared prime, LCM uses the highest power of every prime
How the LCM Calculator works
The least common multiple is the smallest positive number that is a multiple of every number in a set. For two numbers it equals their product divided by their greatest common factor.
When adding fractions, the least common multiple of the denominators is the least common denominator. Using it keeps the numbers as small as possible.
Worked example
For 4, 6 and 10: 4 = 2², 6 = 2 × 3 and 10 = 2 × 5. Taking the highest power of each prime gives 2² × 3 × 5 = 60, the LCM.
Frequently asked questions
How do I find the least common denominator?
Find the LCM of the denominators. For 1/4 and 1/6 the LCM of 4 and 6 is 12, so the fractions become 3/12 and 2/12.
What is the LCM of two prime numbers?
Their product. Primes share no factors, so the LCM of 3 and 7 is 21.
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