What are Multiples of 6?
When the number 6 is multiplied by any natural number, the result is known as a multiple of 6.
For example:
If we multiply 6 by 8, then the product is 48. As a result, we define 48 as a multiple of 6. Another thing to remember here is that the product of two numbers is a multiple of both numbers. Hence, 48 is a multiple of 8 as well.
The multiples of 6 can be expressed in the form of \(6n\), where \(n\) is a natural number.
So for \(n\) = 1, 2, 3, 4, 5, …
The multiples of 6 will be:
6, 12, 18, 24, 30, …
So the \(n\)th multiple of 6 can be obtained by multiplying \(n\) by 6 where \(n\) is a natural number.
Times Table of 6
The multiples of 6 can be arranged in a table known as the times table of 6.
6 \(\times\) 1 | 6 |
6 \(\times\) 2 | 12 |
6 \(\times\) 3 | 18 |
6 \(\times\) 4 | 24 |
6 \(\times\) 5 | 30 |
6 \(\times\) 6 | 36 |
6 \(\times\) 7 | 42 |
6 \(\times\) 8 | 48 |
6 \(\times\) 9 | 54 |
6 \(\times\) 10 | 60 |
The times table of 6 can be extended up to any value of \(n\).
Multiples of 6 by Repeated Addition
Repeated addition means adding a number to itself, in a repetitive manner. Multiplication is a simplified way to add a number repeatedly to itself.
Using repeated addition,
\(n^{th}\) multiple of 6 = 6 + 6 + ……… \(n\) times
We can observe a pattern in these multiples which is the difference between two successive multiples of 6 is 6.
[Note: Memorizing the times table of numbers helps us quickly solve math problems involving repeated addition.]
Rapid Recall
Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, … which can be obtained by multiplying 6 by n or repeated addition of 6 n times where n is any natural number.
Solved Multiples of 6 Examples
Example 1: Is 45 a multiple of 6?
Solution:
List multiples of 6
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …
So, 45 is not a multiple of 6.
Example 2: What is the 14th multiple of 6?
Solution:
The \(n\)th multiple of 6 is given by \(6n\).
So the 14th multiple of 6 can be obtained by multiplying 6 by 14, that is,
6 \(\times\) 14 = 84
Hence 84 is the 14th multiple of 6.
Example 3: Sam, Luke, and Andrew, three friends, decided to buy t-shirts in the order of the first three multiples of 6 respectively. Can you make a list of how many t-shirts each of them bought?
Solution:
The first three multiples of 6 are 6, 12, and 18.
So, Sam bought 6 t-shirts.
Lucifer bought 12 t-shirts.
Andrew bought 18 t-shirts.
Example 4: There are 15 students in a class. If the school decides to give each student 6 stationary kits, how many kits should they purchase?
Solution:
There are 15 students in class and each student will get 6 stationary kits. So, the total number of kits to be purchased is 15th multiple 6.
Therefore, total kits = 6 \(\times\) 15 = 90.
So the school needs to purchase 90 kits.
The multiples of a number are obtained by multiplying the number by a natural number.
If a number is multiplied by another number then the resultant product is known as a multiple and the numbers multiplied are known as factors of the resultant product.
For example, 6 \(\times\) 3 = 18
18 is a multiple of both 3 and 6.
3 and 6 are factors of 18.
The smallest natural number that is a multiple of 6 is 6 itself.
A number can be multiplied indefinitely by an infinite number of natural numbers. So it can have an infinite number of multiples.