Question

The smallest positive integer $n$ for which $864\times n$ is a perfect cube is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

LCM of $864=2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$
$\Rightarrow 2^3\times 2^2\times 3^3$
Hence, for $864\times n$ to be a perfect cube, $n$ must be $2$.