Question

A cuboidal block of $6cm\times 9cm\times 12cm$ is cut up into an exact number of equal cubes. The least possible number of cubes will be

• A. $6$
• B. $9$
• C. $24$
• D. $30$

Answer 1

Answer: (C)

$24$

$\Rightarrow$ Volume of block$=(6\times 9\times 12)c{m}^3=648c{m}^3$

$\Rightarrow$ Side of largest cube $=H.C.Fof6,9,12=3cm$

$\Rightarrow$ Volume of the cube$=(3\times 3\times 3)=27c{m}^3$

$\Rightarrow$ Number of cubes$=\frac{648}{27}=24$