Question

Minimum number of identical cubes having edge length as natural number that can be formed from the cuboid of dimension $12\times 16\times 20$ is

Answer 1

Edge length of the cube will be H.C.F. of $12,16,20$
$12=2^2\times 3$
$16=2^4$
$20=2^2\times 5$
H.C.F. $=2^2=4$
Let the number of cubes that can be formed be $n.$
$\Rightarrow n\times V_{\text{cube}}=V_{\text{cuboid}}$
$\Rightarrow n\times 4^3=12\times 16\times 20$
$\Rightarrow n=60$