Question

Find the smallest number which when multiplied with 5184 will make the product a perfect cube.

• A. 6
• B. 9
• C. 3
• D. 2

Answer 1

The correct option is B 9

Write 5184 as a product of its primes.
$\begin{array}{cc}& \\ 2& 5184\\ 2& 2592\\ 2& 1296\\ 2& 648\\ 2& 324\\ 2& 162\\ 3& 81\\ 3& 27\\ 3& 9\\ & 3\end{array}$

$5184=(2\times 2\times 2)\times (2\times 2\times 2)\times (3\times 3\times 3)\times 3$.

We find that in 5184 one ‘3’ is ungrouped. Thus, to convert 5184 to a perfect cube, we need to multiply it by $3\times 3=9$.