What are the Multiples of 15?
When the number 15 is multiplied by any natural number, the result is known as a multiple of 15.
For example: If we multiply 15 by 3, then the product is 45. As a result, we define 45 as a multiple of 15. Another thing to remember here is that the product of two numbers is a multiple of both the numbers. Hence, 45 is a multiple of 3 as well.
Multiples of 15 can be written as ’15n,’ where n is a natural number, that is, n = 1, 2, 3, 4, 5, 6,……..
So multiples of 15 will be:
15, 30, 45, 60, 75, 90,…
So natural numbers can be multiplied by 15 to get the multiples of 15.
For example: 150, 165 and 180 are all multiples of 15 because we can get these numbers mentioned here by multiplying 15 with some specific natural numbers.
15 × 10 = 150 | 15 multiplied by 10 to get 150 |
|---|---|
15 × 11 = 165 | 15 multiplied by 11 to get 165 |
15 × 12 = 180 | 15 multiplied by 12 to get 180 |
Not only that, we can also observe that the difference between two successive multiples is 15, that is;
30 – 15 = 15, 45 – 30 = 15, 60 – 45 = 15,……..
How to find Multiples by Repeated Addition?
Repeated addition means adding a number to itself, repeatedly. Repeated addition can also be used to determine the multiples of any number.
If we want to find the first six multiples of 15, we can write it in following way:
15 × 1 = 15 | 15 | Here only 15 is added |
|---|---|---|
15 × 2 = 30 | 15 + 15 = 30 | Here 15 added two times |
15 × 3 = 45 | 15 + 15 + 15 = 45 | Here 15 added three times |
15 × 4 = 60 | 15 + 15 + 15 + 15 = 60 | Here 15 added four times |
15 × 5 = 75 | 15 + 15 + 15 + 15 + 15 = 75 | Here 15 added five times |
15 × 6 = 90 | 15 + 15 + 15 + 15 + 15 + 15 = 90 | Here 15 added six times |
The nth Multiple of 15
The nth multiple of 15 can be obtained by either multiplying 15 by n or by adding 15 n times;
nth multiple of 15 = 15 x n, or
nth multiple of 15 = 15 + 15 + ……… n times
[Note: n is any natural number.]
List of the First 10 Multiples of 15
The first ten multiples of 15 are the products of 15 and the first ten natural numbers.
Multiplication | Multiples of 15 |
|---|---|
15 × 1 | 15 |
15 × 2 | 30 |
15 × 3 | 45 |
15 × 4 | 60 |
15 × 5 | 75 |
15 × 6 | 90 |
15 × 7 | 105 |
15 × 8 | 120 |
15 × 9 | 135 |
15 × 10 | 150 |
Multiples and Factors of 15
A factor of 15 is a natural number which when multiplied with another number results in 15. Hence the number 15 is a multiple of its factors.
For example, we know that 3 and 5 are factors of 15. So 15 is a multiple of 3 and 5.
Similarly, 45 is a multiple of 15. So 15 is a factor of 45.
Solved Multiples of 15 Examples
Example 1: Linda, Mary, and Rose, three friends, decided to buy lipsticks in the order of the first three multiples of 15. How many lipsticks did each of them buy?
Solution:
The first three multiples of 15 are 15, 30 and 45.
So, Linda bought 15 lipsticks.
Mary bought 30 lipsticks.
Rose bought 45 lipsticks.
Hence, Linda, Mary, and Rose bought 15, 30, and 45 lipsticks respectively.
Example 2: Is 73 a multiple of 15?
Solution:
List multiples of 15.
15, 30, 45, 60, 75, 90…….….
So, 73 is not a multiple of 15.
Example 3: By division method show that 60 is a multiple of 15?
Solution:
To determine using division method-
Divide 60 by 15 we get,
Hence, 60 is a multiple of the number 15.
Example 4: What is the 5th multiple of 15?
Solution:
The 5th multiple of 15 can be obtained by the repeated addition of 15 for 5 times;
15 + 15 + 15 + 15 + 15
= 75
Hence, the 5th multiple of 15 is 75.
Example 5: Find the 25th multiple of 15.
Solution:
The 25th multiple of 15 can be obtained by multiplying 15 by 25, that is;
15 x 25
= 375
Hence, the 25th multiple of 15 is 375.
The multiples of a number are obtained by multiplying the number with a natural number.
The smallest multiple of 15 is 15 itself.
A number can be multiplied indefinitely so it can have an infinite number of multiples.
The factor of a number is an integer which can evenly divide the number, whereas, the multiple of a number is obtained when the number is multiplied with any natural number.