Least Common Multiple

Least Common Multiple

Learn how to find the Least Common Multiple of two or more numbers in few easy steps.

Step by step guide to finding the Least Common Multiple

  • Least Common Multiple is the smallest multiple that two or more numbers have in common.
  • How to find LCM: list out all the multiples of each number and then find the smallest one they have in common.

Example 1:

Find the LCM for \(8\) and \(6\).

Solution:

Multiples of \(8\): \(8, 16, 24, 32, 40, …\)
Multiples of \(6\): \(6, 12, 18, 24, 30, 36 …\)
LCM \(=24\)

Example 2:

Find the LCM for \(4\) and \(12\).

Solution:

Multiples of \(4\): \(4, 8, 12, 16, 20, …\)
Multiples of \(12\): \(12, 24, 36, 48, …\)
LCM \(=12\)

Example 3:

Find the LCM for \(3\) and \(4\).

Solution:

Multiples of \(3\): \(3,6,9,12,15,18,21,24\)
Multiples of \(4\): \(4,8,12,16,20,24\)
LCM \(=12\)

Example 4:

Find the LCM for \(9\) and \(12\).

Solution:

Multiples of \(9\): \(9,18,27,36,45\)
Multiples of \(12\): \(12,24,36,48\)
LCM \(=36\)

Exercises

Find the LCM for each number pair.

  • \(\color{blue}{4,14}\)
  • \(\color{blue}{5,15}\)
  • \(\color{blue}{16,10}\)
  • \(\color{blue}{4,34}\)
  • \(\color{blue}{8,3}\)
  • \(\color{blue}{12,24}\)

Download Least Common Multiple Worksheet

Answers

  • \(\color{blue}{28}\)
  • \(\color{blue}{15}\)
  • \(\color{blue}{80}\)
  • \(\color{blue}{68}\)
  • \(\color{blue}{24}\)
  • \(\color{blue}{24}\)

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