Question

A cuboidal block of 6 cm $\times$ 9 cm $\times$ 12 cm 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
• E. 45

Answer 1

The correct option is C

24

Volume of block = (6$\times$9$\times$12) cm${}^3$ = 648 cm${}^3$
Side of largest cube = H.C.F. of 6 cm, 9 cm, 12 cm = 3 cm
Volume of this cube = (3$\times$3$\times$3) = 27 cm${}^3$
No. of cubes = 648/27 = 24