LCM Calculator
Find the least common multiple (LCM) of two or more whole numbers. Enter the numbers to see the LCM, the prime factorization of each one, and their greatest common factor.
Least common multiple (LCM)
180
Check the highlighted fields to see your result.
- Greatest common factor (GCF)
- 6
Prime factorization
- 12 = 2² × 3
- 18 = 2 × 3²
- 30 = 2 × 3 × 5
Results are estimates for information only and do not constitute financial, medical, or legal advice.
How to find the LCM
Break each number into prime factors and multiply every prime that appears, each with its largest power. The calculator works it out two numbers at a time with the GCF, which is fast even for large numbers.
The formula
LCM(a, b) = a × b ÷ GCF(a, b)
Worked example
Find the LCM of 12, 18, and 30.
- 12 = 2² × 3, 18 = 2 × 3², 30 = 2 × 3 × 5.
- Take each prime with its largest power: 2², 3², and 5.
- LCM = 4 × 9 × 5 = 180.
Frequently asked questions
What is the LCM used for?
Adding and subtracting fractions: the LCM of the denominators is the least common denominator. It also answers timing questions, like when two buses that leave every 12 and 18 minutes will leave together again (every 36 minutes).
How are the GCF and LCM related?
For two numbers, GCF × LCM = the product of the numbers. For example, 12 and 18 have a GCF of 6 and an LCM of 36, and 6 × 36 = 12 × 18 = 216. This only works for two numbers, not three or more.
Can the LCM be smaller than the numbers?
No. The LCM is a multiple of every number, so it's always at least as large as the largest one. If one number is a multiple of all the others, that number is the LCM.