Find the smallest possible integer m such that 54m is a cube number?

Apr 24, 2018

$m = 4$

Explanation:

$54 = 2 \cdot {3}^{3}$

$\sqrt[3]{54 m} = \sqrt[3]{2 \cdot {3}^{3} m}$

$= 3 \sqrt[3]{2 m}$

least cubic numbers are $1 \mathmr{and} 8$

but $1$ is not possible as $m$ must be an integer

So,

$2 m = 8$color(green)(rarr$m = 4$

$54 \cdot 4 = 216$
$216 = {6}^{3}$