Question

Write the cubes of 5 natural numbers which are multiples of 3 and verify the followings:
'The cube of a natural number which is a multiple of 3 is a multiple of 27'

Answer 1

Five natural numbers, which are multiples of 3, are 3, 6, 9, 12 and 15.
Cubes of these five numbers are:

\[3^3 = 3 \times 3 \times 3 = 27\]

\[ 6^3 = 6 \times 6 \times 6 = 216\]

\[ 9^3 = 9 \times 9 \times 9 = 729\]

\[ {12}^3 = 12 \times 12 \times 12 = 1728\]

\[ {15}^3 = 15 \times 15 \times 15 = 3375\]

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

\[27 = 27 \times 1\]

\[216 = 27 \times 8\]

\[729 = 27 \times 27\]

\[1728 = 27 \times 64\]

\[3375 = 27 \times 125\]

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.