What are the Multiples of 60
When the number 60 is multiplied by any natural number, the result is known as a multiple of 60.
For example, if we multiply 60 by 3, the product is 180. As a result, we define 180 as a multiple of 60. Another thing to remember here is that the product of two numbers is a multiple of both the numbers. Hence, 60 is a multiple of 3 as well.
The multiples of 60 can be written as ’60n,’ where n is a natural number, that is, n=1, 2, 3, 4, 5, 6,……..
So, the multiples of 60 will be:
60, 120, 180, 240, 300, 360,…
Therefore, natural numbers can be multiplied by 60 to get the multiples of 60.
For example, 180, 300 and 420 are all multiples of 60 because we can get these numbers mentioned here by multiplying 60 with some specific natural numbers.
We can also observe that the difference between two successive multiples is 60, that is:
120 – 60 = 60, 180 – 120 = 60, 240 – 180 = 60,……..
How can we find the 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 60, we can write it in the following way:
The nth Multiple of 60
The nth multiple of 60 can be obtained by either multiplying 60 by n or by adding 60n times:
nth multiple of 60 = 60 x n, or
nth multiple of 60 + 60 + 60 + ……. n times
[Note: n is any natural number]
List of the First 10 Multiples of 60
The first ten multiples of 60 are the products of 60 and the first ten natural numbers.
Multiples and Factors of 60
A factor of 60 is a natural number that, when multiplied with another number, results in 60. Hence, the number 60 is a multiple of its factors.
For example, we know that 3 and 5 are the factors of 60. So, 60 is a multiple of 3 and 5.
Similarly, 180 is a multiple of 60. So, 60 is a factor of 180.
Solved Multiples of 40 Examples
Example 1: Three friends, Linda, Mary and Rose, decided to buy antique marbles in the order of the first three multiples of 60. How many marbles did each of them buy?
Solution:
The first three multiples of 60 are 60, 120 and 180.
So, Linda bought 60 marbles.
Mary bought 120 marbles.
Rose bought 180 marbles.
Hence, Linda, Mary and Rose bought 60, 120 and 180 marbles, respectively.
Example 2: Is 192 a multiple of 60?
Solution:
List the multiples of 60.
60, 120, 180, 240, 300, 360 ……, ….
So, 192 is not a multiple of 60.
Example 3: How can we show that 180 is a multiple of 60 through the division method?
Solution:
We can determine this by using the division method through the following way:
On dividing 180 by 60, we get,
Hence, 180 is a multiple of the number 60.
Example 4: What is the 5th multiple of 60?
Solution:
The 5th multiple of 60 can be obtained by the repeated addition of 60 five times:
60 + 60 + 60 + 60 + 60
= 300
Hence, the 5th multiple of 60 is 300.
Example 5: Find the 25th multiple of 60.
Solution:
The 25th multiple of 60 can be obtained by multiplying 60 by 25:
60 x 25
= 1500
Hence, the 25th multiple of 60 is 1500.
The multiples of a number are obtained by multiplying the number by a natural number.
The smallest multiple of 60 is 60 itself.
A number can be multiplied indefinitely, so it can have an infinite number of multiples.
The multiples of the number 60 are the numbers that we get when 60 is multiplied by any natural number. The multiples of 60 can be expressed in the form of 60n, where n is a natural number.
The multiples of 60 are 60, 120, 180…, Therefore, 100 is not a multiple of 60.