Question

Find the smallest number by which the number $108$ must be multiplied to obtain a perfect cube.

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is A $2$

Prime factorising $108$, we get,

$108=3\times 3\times 3\times 2\times 2$

$=3^3\times 2^2$.

We know, a perfect cube has multiples of $3$ as powers of prime factors.

Here, number of $3$'s is $3$ and number of $2$'s is $2$.

So we need to multiply another $2$ to the factorization to make $108$ a perfect cube.

Hence, the smallest number by which $108$ must be multiplied to obtain a perfect cube is $2$.

Hence, option $A$ is correct.