Least Common Multiple of 2 Numbers

Definitions

The multiple of a number is that number multiplied by an integer. The multiples of a number are found by multiplying it with 1, 2, 3, 4….and so on.

For example, the multiples of 4 are 4 × 1, 4 × 2, 4 × 3, 4 × 4,…or 4, 8, 12, 16 …and so on.

The multiples of two numbers that are common to both the numbers are known as common multiples of those numbers.

The smallest positive number that is a common multiple of two numbers is the least common multiple or lcm of those two numbers.

The least common mulitple of two numbers is also the smallest number that both the numbers divide completely without leaving a remainder.

Rules to find the least common multiple of two numbers

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

Example

Find the least common multiple of 8 and 10

Solution

Step 1:

The multiples of 8 and 10 are as follows

Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80…

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

Step 2:

The first common multiple of 8 and 10 is 80, which is their least common multiple lcmProblem 1:

Find the least common multiple of 12 and 18

Solution

Step 1:

The multiples of 12 and 18 are as follows

Multiples of 12 = 12, 24, 36 , 48, 60, 72, 84…

Multiples of 18 = 18, 36, 54, 72, 90, 108…

Step 2:

The first common multiple of 12 and 18 is 36, which is their least common multiple lcmProblem 2:

Find the least common multiple of 9 and 15

Solution

Step 1:

The multiples of 9 and 15 are as follows

Multiples of 9 = 9, 18, 27, 36, 45, 54…

Multiples of 15 = 15, 30, 45, 60…

Step 2:

The first common multiple of 9 and 15 is 45, which is their least common multiple lcm