LCM Calculator

LCM calculator and least common multiple calculator for 2 to 20 numbers. Find the least common multiple (also called the lowest common multiple) with prime factorization and GCF steps that show how to find the LCM.

Updated

LCM(8, 12, 20) = 120

Greatest common factor: GCF(8, 12, 20) = 4

Prime factorization method

  • 8 = 2 × 2 × 2
  • 12 = 2 × 2 × 3
  • 20 = 2 × 2 × 5

Take the highest power of each prime that appears in any number:

LCM = 23 × 3 × 5 = 2 × 2 × 2 × 3 × 5 = 120

GCF method

LCM(a, b) = a × b ⁄ GCF(a, b). With more than two numbers, take the LCM of the first two, then the LCM of that result and the next number.

  1. GCF(8, 12) = 4, so LCM = 8 × 12 ⁄ 4 = 24
  2. GCF(24, 20) = 4, so LCM = 24 × 20 ⁄ 4 = 120

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What is the least common multiple?

The least common multiple (LCM), also called the lowest common multiple, of two or more whole numbers is the smallest positive number that every one of them divides into evenly. For example, the multiples of 4 are 4, 8, 12, 16, … and the multiples of 6 are 6, 12, 18, …, so LCM(4, 6) = 12.

This LCM calculator, also a lowest common multiple calculator, takes 2 to 20 positive whole numbers up to one trillion and shows the least common multiple, the greatest common factor (GCF), and the steps of each method below.

How to find the LCM

1. Prime factorization

Break each number into prime factors, then multiply the highest power of every prime that appears in any of them. For 8, 12, and 20:

  • 8 = 2 × 2 × 2 = 2³
  • 12 = 2 × 2 × 3 = 2² × 3
  • 20 = 2 × 2 × 5 = 2² × 5

The highest powers are 2³, 3, and 5, so LCM(8, 12, 20) = 8 × 3 × 5 = 120.

2. Greatest common factor

For two numbers, LCM(a, b) = a × b ⁄ GCF(a, b). For more numbers, work in pairs: LCM(8, 12) = 96 ⁄ 4 = 24, then LCM(24, 20) = 480 ⁄ 4 = 120. This is the fastest method for large numbers, and it is how the calculator finds the exact LCM even when the answer is far larger than the numbers you entered.

3. Listing multiples

Write out multiples of each number until one shows up in every list. It works well for small numbers, and the result shows these lists whenever they are short enough to read.

What the result includes

  • The least common multiple of all the numbers.
  • The greatest common factor, the largest number that divides all of them.
  • The prime factorization of each number and of the LCM.
  • The GCF steps, pair by pair.
  • The lists of multiples, when the LCM is at most 12 times the smallest number.

Frequently asked questions

What is the LCM of 12 and 18?

36. Since 12 = 2² × 3 and 18 = 2 × 3², the LCM is 2² × 3² = 36. You can check it with the GCF method too: 12 × 18 ⁄ 6 = 36.

How is the LCM used with fractions?

The least common denominator of two fractions is the LCM of their denominators. To add 1⁄6 + 3⁄8, use LCM(6, 8) = 24: 4⁄24 + 9⁄24 = 13⁄24.

What is the difference between the LCM and the GCF?

The LCM is the smallest number that all of your numbers divide into; the GCF is the largest number that divides all of them. For two numbers, LCM × GCF equals the product of the numbers.

What if the numbers have no common factors?

When two numbers have a GCF of 1, they are called relatively prime, and their LCM is simply their product. For example, LCM(8, 9) = 72. With three or more numbers, a GCF of 1 is not enough: LCM(2, 3, 4) = 12, not 24, because 2 and 4 share a factor.

What's changed
  • Launched.

References