Least Common Multiple of 3 Numbers

Introduction

Finding the least common multiple lcm of three numbers is similar to finding the lcm of 2 numbers.

To find the least common multiple lcm of three numbers

• We begin by listing the first few multiples of the three numbers.
• Then we look for the common multiples of all the numbers.
• The first common multiple of the numbers would be their least common multiple.

Problem 1:

Find the least common multiple of 6, 10, 15

Solution

Step 1:

The multiples of 6, 10 and 15 are as follows

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80

Multiples of 15 = 15, 30, 45, 60, 75, 90

Step 2:

Some common multiples of the three numbers are 30, 60…

Step 3:

The first common multiple of 6, 10 and 15 is 30, which is their least common multiple lcmProblem 2:

Find the least common multiple of 9, 12, 24

Solution

Step 1:

The multiples of 9, 12 and 24 are as follows

Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72

Multiples of 12 = 12, 24, 36, 48, 60, 72

Multiples of 24 = 24, 48, 72, 96

Step 2:

The first common multiple of 9, 12 and 24 is 72, which is their least common multiple lcm