About this LCM calculator
The least common multiple (LCM) of a set of whole numbers is the smallest positive number that each of them divides into exactly. It gives the lowest common denominator when adding fractions, and answers timing questions such as when two repeating events next happen on the same day. This calculator shows four methods side by side: multiplying the highest power of every prime factor, dividing the numbers down a ladder of primes, using the formula LCM(a, b) = a × b ÷ GCD(a, b) one pair at a time, and listing multiples until they meet. Results are exact for numbers of any size the tool accepts.
How to find the least common multiple
- Enter your numbers. Type 2 to 15 positive whole numbers separated by commas or spaces, or press an example.
- Press Find LCM. The LCM is shown along with the greatest common factor of the same numbers.
- Follow the method you need. Check the prime factorization, the ladder, the GCD formula, or the lists of multiples, where the LCM is highlighted.
Frequently asked questions
What is the LCM of 12 and 18?
It is 36. The multiples of 12 are 12, 24, 36, and so on, and those of 18 are 18, 36, and so on; 36 is the first number in both lists. With primes: 12 = 2² × 3 and 18 = 2 × 3², so the LCM is 2² × 3² = 36.
How are LCM and GCF related?
For two numbers, LCM × GCF = the product of the numbers. For 12 and 18, the GCF is 6, so the LCM is 12 × 18 ÷ 6 = 36. This shortcut does not hold directly for three or more numbers.
How does the ladder method work?
Write the numbers in a row and divide by a prime that goes into at least one of them, carrying down any number it does not divide. Repeat until every number is 1, then multiply all the primes on the left.
How is the LCM used with fractions?
The LCM of the denominators is the lowest common denominator. To add 1/4 and 1/6, use LCM(4, 6) = 12, so the sum is 3/12 + 2/12 = 5/12.
What is the LCM of the numbers 1 to 10?
It is 2520, the smallest number that every whole number from 1 to 10 divides exactly. It equals 2³ × 3² × 5 × 7.