Question

The least number that should be multiplied to $2^{18}\times 3^{19}$ to make it a perfect cube is

• A. 3
• B. 6
• C. 9
• D. 18

Answer 1

Answer: (C)

9

$2^{18}\times 3^{19}=2^{18}\times 3^{18}\times 3$

$={\left(2^6\right)}^3\times {\left(3^6\right)}^3\times 3$

$3^2$ should be multiplied to get a perfect cube.

$={\left(2^6\right)}^3\times {\left(3^6\right)}^3\times 3\times 3^2$

$={\left(2^6\right)}^3\times {\left(3^6\right)}^3\times 3^3$ which is a perfect cube

Hence $3^2=9$ should be multiplied to get a perfect cube.