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.
First 10 Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 |
For example, 9, 16, 900 and 99 are all multiples of 9 for the following reasons
81 | = | 9 | x | 9 |
18 | = | 9 | x | 2 |
900 | = | 9 | x | 100 |
99 | = | 9 | x | 11 |
(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:
Multiplication of 9 with Natural Numbers | Multiples of 9 |
9 x 1 | 9 |
9 x 2 | 18 |
9 x 3 | 27 |
9 x 4 | 36 |
9 x 5 | 45 |
9 x 6 | 54 |
9 x 7 | 63 |
9 x 8 | 72 |
9 x 9 | 81 |
9 x 10 | 90 |
9 x 11 | 99 |
9 x 12 | 108 |
9 x 13 | 117 |
9 x 14 | 126 |
9 x 15 | 135 |
9 x 16 | 144 |
9 x 17 | 153 |
9 x 18 | 162 |
9 x 19 | 171 |
9 x 20 | 180 |
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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Frequently Asked Questions on Multiples of 9
What are the multiples of 9?
The multiples of 9 are the numbers that are obtained from multiplying 9 with the integers.
What are the first 10 multiples of 9?
The first 10 multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.
What is the least common multiple of 9 and 18?
The least common multiple of 9 and 18 is 18.
Write the multiples of 9 between 20 and 40?
The multiples of 9 between 20 and 40 are 27 and 36.
What are the multiples of 9 that lies between 50 and 100?
The multiples of 9 that lies between 50 and 100 are 54, 63, 72, 81, 90 and 99.