A rectangular block measuring 8 cm by 12 cm by 16 cm is cut into an exact number of cubes of equal size. What will be the least possible number of cubes?

Question: A rectangular block measuring 8 cm by 12 cm by 16 cm is cut into an exact number of cubes of equal size. What will be the least possible number of cubes?

Solution:
Given that,
Sides of the rectangular block = 8 cm, 12 cm, 16 cm

Let n be the number of cubes.
HCF( 8, 12, 16) = 4 cm
And side of the square = 4 cm

We know,
Volume of the cuboid = n × Volume of the cube
⇒ Length × breadth × height = n × side³
⇒ 8 × 12 × 16 = n × 4 × 4 × 4
⇒ 64n = 8 × 12 × 16
⇒ n = (8 × 12 × 16)/64
∴ n = 24

So the number of cubes is 24.