Question

Find the smallest number by which $135$ must be divided to obtain a perfect cube.
[3 marks]
[NCERT - Ex 7.1, Q3 (iii)]
[Smallest Multiple that is a Perfect Cube]

• A. 5
• B. 3
• C. 2
• D. 6

Answer 1

The correct option is A 5

Solution:
$\begin{array}{cc}3& 135\\ 3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}$
Prime factors of $135=3\times 3\times 3\times 5$
[2 marks]

Here one factor $5$ does not appear in a triplet.
Therefore, $135$ must be divided by $5$ to make it a perfect cube.
[1 mark]