LCM Calculator

Find the least common multiple of two or more whole numbers, with every step shown so you can check the work.

Enter two or more whole numbers, separated by commas or spaces.
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LCM
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Prime factorization method
    Euclidean algorithm

      What is the least common multiple?

      A multiple of a number is what you get when you multiply it by 1, 2, 3 and so on. The multiples of 4 are 4, 8, 12, 16, 20, 24… and the multiples of 6 are 6, 12, 18, 24… The numbers both lists share, 12, 24, 36 and onward, are common multiples. The smallest of them, 12, is the least common multiple.

      How to use the LCM calculator

      1. Type two or more whole numbers, separated by commas or spaces.
      2. The LCM appears instantly, along with the working.
      3. For two numbers, you also see the Euclidean algorithm method.

      Method 1: Prime factorization

      Break each number into prime factors, then multiply every prime that appears, using the highest power it has in any of the numbers.

      Take 12, 15 and 20:

      • 12 = 2² × 3
      • 15 = 3 × 5
      • 20 = 2² × 5

      The primes are 2, 3 and 5. The highest powers are 2², 3 and 5, so the LCM is 4 × 3 × 5 = 60.

      Method 2: Using the GCF

      For two numbers, the quickest route is this formula:

      LCM(a, b) = (a × b) ÷ GCF(a, b)

      For 36 and 48, the greatest common factor is 12, so the LCM is (36 × 48) ÷ 12 = 1,728 ÷ 12 = 144. You can find the GCF with our GCF calculator.

      Method 3: Listing multiples

      For small numbers you can list multiples until you find a match. The multiples of 8 are 8, 16, 24, 32, 40, 48 and of 12 are 12, 24, 36, 48. The first shared one is 24. This method is easy to understand but slow for larger numbers.

      Where the LCM is used

      • Adding and subtracting fractions: the LCM of the denominators is the least common denominator.
      • Scheduling: if one bus leaves every 12 minutes and another every 15 minutes, they leave together every 60 minutes, the LCM of 12 and 15.
      • Repeating events: lights blinking every 4 and 6 seconds blink together every 12 seconds.

      Last reviewed October 2026.

      Frequently asked questions

      What does LCM stand for?

      LCM stands for least common multiple, also called the lowest common multiple. It is the smallest positive number that every number in your list divides into evenly.

      What is the LCM of two prime numbers?

      Two different primes share no factors, so their LCM is simply their product. For example, the LCM of 7 and 11 is 77.

      How is the LCM related to the GCF?

      For two numbers, LCM × GCF equals the product of the numbers. So LCM(a, b) = (a × b) ÷ GCF(a, b). For 12 and 18, the GCF is 6, so the LCM is 216 ÷ 6 = 36.

      Can the LCM be one of the numbers?

      Yes. If one number is a multiple of all the others, it is the LCM. The LCM of 4, 8 and 16 is 16.

      How do I use the LCM to add fractions?

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

      Can I find the LCM of more than two numbers?

      Yes. Enter as many whole numbers as you like. The calculator finds the LCM of the first two, then the LCM of that result and the next number, and so on.