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Question

Write cubes of five natural numbers which are multiples of 3 and verify the following the cube of a natural number which is a multiple of 3 is a multiple of 27


Solution

Five natural numbers, which are multiples of 3, are 3, 6, 9, 12 and 15.

Cubes of these five numbers are:

3³ = 3 x 3 x 3 = 27

6³ = 6 x 6 x 6 = 216

9³ = 9 x 9 x 9 = 729

12³ = 12 x 12 x 12 = 1728

15³ = 15 x 15 x 15 = 3375

Now, let us write the cubes as a multiple of 27. We have:

27 = 27 x 1

216 = 27 x 8

729 = 27 x 27

1728 = 27 x 64

3375 = 27 x 125

It is evident that the cubes of the above multiples of 3 could be written as multiples of 27. Thus, it is verified that the cube of a natural number, which is a multiple of 3, is a multiple of 27.

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