What are the Multiples of 30?
The multiples of the number 30 are those numbers that we get as a result of multiplying 30 by any natural number.
For example, if we multiply 30 by 2, the product will be 60. So, we say that 60 is a multiple of 30.
The multiples of 30 can be expressed in the form of 30n, where n is a natural number.
So for n = 1, 2, 3, 4, 5, 6, …
The multiples of 30 will be:
30, 60, 90, 120, 150, 180, …
So the nth multiple of 30 can be obtained by multiplying n by 30 where n is a natural number.
Times Table of 30
The multiples of 30 can be arranged in a table known as the times table of 30.
30 x 1 | 30 |
30 x 2 | 60 |
30 x 3 | 90 |
30 x 4 | 120 |
30 x 5 | 150 |
30 x 6 | 180 |
30 x 7 | 210 |
30 x 8 | 240 |
30 x 9 | 270 |
30 x 10 | 300 |
The times table of 30 can be extended up to any value of n.
Multiples of 30 by Repeated Addition
Repeated addition indicates that we are adding a number to itself, in a repetitive manner. Multiplication is a simplified way to add a number repeatedly to itself.
Using repeated addition,
The nth multiple of 30 = 30 + 30 + ……… n times
We can observe a pattern in these multiples, and that is the difference between two successive multiples of 30, is 30.
[Note: Memorizing the times table of numbers helps us to quickly solve math problems involving repeated addition. ]
Rapid Recall
Solved Multiples of 30 Examples
Example 1: Is 50 a multiple of 30?
Solution:
List the multiples of 30.
30, 60, 90, 120, …
So, 50 is not a multiple of 30.
Example 2: How can the division method be used to show that 60 is a multiple of 30?
Solution:
To determine using the division method:
Dividing 60 by 30, we get,
\(\frac{60}{30}=2\) and no remainder is left after the division operation.
Hence, 60 is a multiple of the number 30.
Example 3: Ronny buys some packets of orange candies for $15 per packet. Frank buys some packets of chocolate candies for $30 per packet. Ronny and Frank spend the same amount of money on the candies. What is the minimum amount of money they could have spent?
Solution:
Price of orange candies bought by Ronny is $15 per packet
Price of chocolate candies bought by Frank is $30 per packet
Since both Ronny and Frank spent the same amount of money on the candies, the total amount spent by each of them is a common multiple of 15 and 30.
Let us list the multiples of 15 and 30
Multiples of 15: 15, 30, 45, 60, 75, 90 …..
Multiples of 30: 30, 60, 90, 120,..
So the common multiples of 15 and 30 are 30, 60, 90,…
The lowest of these common multiples is 30.
Therefore, the minimum amount they could have spent is $30.
A multiple is defined as a number which we get by multiplying a counting number by another number.
The first 10 multiples of 30 are:
30, 60, 90, 120, 150, 180, 210, 240, 270, 300.
So, the 6th multiple of 30 is 180.
The factor of a number is a natural number that can evenly divide the original number. On the other hand, the multiple of a number is obtained when a number is multiplied by any natural number.
The multiples of the number 30 are the numbers that we get when 30 is multiplied by any natural number. The multiples of 30 can be expressed in the form of 30n, where n is a natural number.
A number can have an infinite number of multiples as there are an infinite set of natural numbers that can be multiplied with any given number.