Write the cubes of 5 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.

Given:

The cube of a natural number which is a multiple of 3 is a multiple of 27.

To do:

We have to write the cubes of 5 natural numbers which are multiples of 3 and verify the given statement.

Solution:

First 5 natural numbers which are multiples of 3 are $3,6,9,12,15$.

Therefore,

$(3)^3=3\times3\times3=27$

$=27\times1$

$(6)^3=6\times6\times6=216$

$=27\times8$

$(9)^3=9\times9\times9=729$

$=27\times27$

$(12)^3=12\times12\times12=1728$

$=27\times64$

$(15)^3=15\times15\times15=3375$

$=27\times125$

$27, 216, 729, 1728, 3375$ are multiples of 27.

Hence, the given statement is true.

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