Ravi made a cuboid of plasticine of dimensions 12cm, 8cm and 3cm. How many minimum numbers of such cuboids will be needed to form a cube?

Given, a cubiod with sides as 12cm, 8 cm and 3cm

To find out number of cuboids required to form a cube.

Volume of the cubiod = 12 × 8 × 3 cm³

The cube is formed by stacking many such cuboids and it will have side lengths which are multiple of 12,8,3 cm

The smallest such cube will have a side length of LCM(12,8,3)

LCM is found out as follows:

LCM is 3 × 4 × 2 = 24 cm

And a volume = (24 × 24 × 24)cm

∴ Number of cuboids to fit in a cube =

= 2 × 24

= 48

Hence, 48 cuboids are needed to form a cube