LCM Calculator

Enter two or more whole numbers to find their least common multiple (LCM), with the prime factorization method and a list of multiples shown step by step.

What is the least common multiple?

The least common multiple (LCM) of two or more numbers is the smallest positive number that each of them divides into exactly. The LCM of 4 and 6 is 12, because 12 is the first number in both lists of multiples. You use the LCM to find a common denominator when adding fractions, or to work out when repeating events line up.

How to find the LCM

Method 1: list the multiples

Write out multiples of each number until you find one they share. Multiples of 4 are 4, 8, 12, 16 … and multiples of 6 are 6, 12, 18 …, so the LCM is 12. This works well for small numbers.

Method 2: prime factorization

Break each number into prime factors.
For each prime, take the highest power that appears.
Multiply those powers together.

For 4, 6 and 15: 4 = 2², 6 = 2 × 3 and 15 = 3 × 5. The highest powers are 2², 3 and 5, so the LCM is 4 × 3 × 5 = 60.

Method 3: use the GCF

LCM(a, b) = a × b ÷ GCF(a, b)

For 8 and 12, the GCF is 4, so the LCM is 8 × 12 ÷ 4 = 24. Find the GCF with our GCF calculator.

Numbers	LCM
2 and 3	6
3 and 4	12
4 and 6	12
6 and 8	24
8 and 12	24
12 and 18	36
2, 3 and 4	12
3, 4 and 5	60

Frequently asked questions

What is the LCM of 6 and 8?

24. Multiples of 6 are 6, 12, 18, 24 and multiples of 8 are 8, 16, 24, so 24 is the first common multiple.

What is the LCM of 3, 4 and 5?

60, because 3, 4 and 5 share no common factors, so the LCM is their product.

What is the difference between LCM and GCF?

The LCM is the smallest number that all the numbers divide into. The GCF is the largest number that divides into all of them.

How is the LCM used with fractions?

The LCM of the denominators is the least common denominator. To add 1/4 and 1/6, use 12: 3/12 + 2/12 = 5/12.

Can the LCM be one of the numbers?

Yes. If one number is a multiple of the others, it is the LCM. The LCM of 3 and 12 is 12.