What are the Multiples of 12?
The multiples of 12 are those numbers that we get as a result of multiplying 12 by any natural number.
Example: If we multiply 12 by 3, the product will be 36. So, we can say that 36 is a multiple of 12 and 3.
The multiples of 12 can be expressed in the form of 12n, where, n is any natural number, n = 1, 2, 3, 4, 5, 6, …
The multiples of 12 will be:
12, 24, 36, 48, 60, 72, and so on.
Also, we can observe that the difference between each succeeding number and the preceding number is 12, that is,
24 – 12 = 12
36 – 24 = 12
48 – 36 = 12, and so on.
For example, 132, 96, and 144 are all multiples of 12 because we can get all these numbers by multiplying 12 by a natural number.
12 × 11 = 132 | 12 is multiplied by 11 to get 132 |
|---|---|
12 × 8 = 96 | 12 is multiplied by 8 to get 96 |
12 × 12 = 144 | 12 is multiplied by 12 to get 144 |
The 12 times table can be written as:
How can we Find the Multiples by Repeated Addition?
Repeated addition is the process of adding the same number multiple times.
We can find the multiples through repeated addition in the following way:
Rapid Recall
The multiples of 12 are:
Solved Examples
Example 1: Four friends, John, Max, Sam, and Ruth, decided to buy chocolates in the order of the first four multiples of 12, respectively. How many chocolates did each of them buy?
Solution:
The first four multiples of 12 are 12, 24, 36, and 48.
So,
John bought 12 chocolates.
Max bought 24 chocolates.
Sam bought 36 chocolates.
Ruth bought 48 chocolates.
Hence, John, Max, Sam, and Ruth bought 12, 24, 36, and 48 chocolates, respectively.
Example 2: Is 60 a multiple of 12?
Solution:
List the multiples of 12.
12, 24, 36, 48, 60, 72, and so on. The list includes 60.
Also, \(\frac{60}{12}\) = 5 R0, the remainder is 0 when 60 is divided by 12.
So, 60 is a multiple of 12.
Example 3: Show that 120 is a multiple of 12.
Solution:
On dividing 120 by 12, we get,
Here, the remainder is 0, when 120 is divided by 12.
Hence, 120 is a multiple of 12.
Example 4: What is the 7\(^{th}\) multiple of 12?
Solution:
The 7\(^{th}\) multiple of 12 can be obtained by the repeated addition of 12 seven times:
12 + 12 + 12 + 12 + 12 + 12 + 12 = 84
Hence, the 7\(^{th}\) multiple of 12 is 84.
Example 5: Is 75 a multiple of 12?
Solution:
List the multiples of 12.
12, 24, 36, 48, 60, 72, 84, and so on. The list does not contain 75.
Also, \(\frac{75}{12}\) = 6 R3, the remainder is 3 when 75 is divided by 12.
So, 75 is not a multiple of 12.
A multiple of a number is defined as the product we get by multiplying a number by any natural number.
The first 10 multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120.
So, the 6th multiple of 12 is 72.
The multiples of 12 are the numbers that we get when 12 is multiplied by any natural number. The multiples of 12 can be expressed in the form of 12n, where n is a natural number.
A number can have an infinite number of multiples as there is an infinite count of natural numbers to be multiplied with.
The multiples of 12 will be obtained by multiplying natural numbers, that is, 1, 2, 3, 4, 5, and so on, by 12.
The multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so on.
The factors of 12 are the exact divisors of 12.
The factors of 12 = 1, 2, 3, 4, 6, and 12
There can be infinite multiples of a number, whereas the factors are finite.