A cuboidal block, 12 cm by 24 cm by 30 cm, is cut up into an exact number of identical cubes. The least possible number of such cubes is:

Correct option is B

Given:

​A cuboidal block, 12 cm by 24 cm by 30 cm,

Formula used:

Volume of cuboid = l × w × h 

where, l is length, w is width, h is height  

Volume of cube = $$\text{Side}^3$$​​

Solution:

Length of cuboidal block = 12 cm

Width of cuboidal block = 24 cm

Height of cuboidal block = 30 cm

Volume = 12 x 24 x 30

= 8640$$cm^3$$

Now, we need to find the least possible number of identical cubes.

So, we will find H.C.F. of 12 , 24, 30 = 6

So, Side of cube becomes 6 cm

Therefore, Volume of cubes is given by

​$$side^3$$ = $$6^3$$ = 216$$cm^3$$

So, Least possible number of identical cubes is given by

 = $$\frac{volume\ of \ cuboidal\ block}{Volume\ of\ cube}$$

= $$\frac{8640}{216}$$

= 40 

The least possible number of such cubes is: 40