Multiples of 9

In Mathematics, the multiples of 9 are the numbers that are completely divisible by 9 without leaving any remainder. In other words, the multiple of 9 is the product of 9 with any natural number. For example, 27 is a multiple of 9, as it is the product of 9 and 3. Some of the examples of multiples of 9 include 9, 18, 56, 90, 900, and so on. In this article, we are going to learn what are the multiples of 9, a list of multiples of 9 with many solved examples in a detailed way.

What are the Multiples of 9?

Any number that can be denoted in the form 9n where n is a natural number, is a multiple of 9. So if two values p and q are there, we say that q is a multiple of p if q = np. In other words, the multiples of 9 are the numbers that leave no remainder (i.e. Remainder = 0), when it is divided by 9. 

For example, 9, 16, 900 and 99 are all multiples of 9 for the following reasons

(i.e) 81/9 = 9 and remainder is 0

18/9 = 2 and remainder is 0

900/9 = 100 and remainder is 0.

99/9 = 11 and remainder is 0.

Since the numbers are exactly divided by 9, the numbers 81, 18, 900, 99 are multiples of 9.

Also, read: Multiple of a Number

First 20 Multiples of 9

The list of first 20 multiples of 9 are as follows:

Video Lesson on Common Multiples

Multiples of 9 Examples

Example 1: 

Find out the multiples of 9 from the list of numbers 18, 35, 54, 62, 81 and 91.

Solution:

Given that list of numbers are 18, 35, 54, 62, 81 and 91.

We know that the multiples of 9 are the numbers that are exactly divisible by 9.

Hence, the multiples of 9 are 18, 54 and 81.

But, the numbers 35, 62 and 91 are not the multiples of 9 as they leave some remainder value.

Example 2:

What is the least common multiple of 8 and 9?

Solution:

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

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

Hence, the least common multiple of 8 and 9 is 72.

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