LCM Calculator
Find the least common multiple of two or more numbers, with prime factorization and step-by-step work. Free and instant.
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About the LCM Calculator
The least common multiple (LCM) of several numbers is the smallest positive number that every one of them divides evenly. It is the key to adding fractions with different denominators and to scheduling problems. This calculator takes two or more numbers, shows the prime factorization of each, and builds the LCM from the highest power of each prime.
For the greatest common factor use the GCF calculator.
How to use it
- Type two or more positive whole numbers, separated by commas or spaces.
- Press Find LCM.
- Read the LCM and the prime factorization steps.
How to find the LCM
- Prime factorization: factor each number, then multiply every prime that appears, using its highest power.
- GCF method: for two numbers, LCM(a, b) = a × b ÷ GCF(a, b).
- Listing multiples: list multiples of each number and pick the smallest one they share.
Example: LCM(12, 18). 12 = 22 × 3 and 18 = 2 × 32, so LCM = 22 × 32 = 36.
LCM examples
| Numbers | LCM |
|---|---|
| 4 and 6 | 12 |
| 8 and 12 | 24 |
| 12 and 18 | 36 |
| 5 and 7 | 35 |
| 6, 8 and 12 | 24 |
| 3, 4 and 5 | 60 |
Frequently asked questions
What is the LCM of two numbers?
The smallest positive number that both numbers divide into evenly. For 4 and 6 it is 12.
How do I use the LCM to add fractions?
Use the LCM of the denominators as the common denominator, convert each fraction, then add the numerators.
What is the LCM of two prime numbers?
Their product. For example LCM(5, 7) = 35.
What is the relationship between LCM and GCF?
For two numbers, LCM × GCF = a × b. So LCM = a × b ÷ GCF.
Can I find the LCM of three or more numbers?
Yes. Enter them all. The calculator combines them using the highest power of every prime.
Last reviewed: November 2026.
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