Module 3 · Factors and multiples · Lesson 11 of 39

Least common multiple (LCM)

The smallest number both numbers divide into.

In this lesson · about 12 minutes

  • Find the LCM by listing multiples
  • Find the LCM with prime factorizations
  • Check an LCM

A common multiple of two numbers is divisible by both. The least common multiple (LCM) is the smallest one. The LCM of 2 and 3 is 6; the LCM of 2 and 4 is 4.

Method 1: list the multiples of the larger number

For 3 and 4: 4 · 1 = 4 (3 doesn't divide it), 4 · 2 = 8 (no), 4 · 3 = 12 (yes!). The LCM is 12.

Method 2: prime factorizations

For bigger numbers, factor both and take each prime the most times it appears in either one.

Worked example

LCM of 20 and 75

Use prime factorizations.

    Step 0 of 5

    Try it · interactive

    Multiples and factors side by side

    Change the numbers. The first number on both multiple lists is the LCM.

    Multiples (for the LCM)

    6:6121824303642485460
    8:8162432404856647280

    Factors (for the GCF)

    6:1236
    8:1248

    LCM = 24, the first number on both multiple lists. By primes: 2 · 3 and 2³.

    GCF = 2, the biggest number on both factor lists.

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