Question

The length, breadth and height of a box is 84 cm, 116 cm and 172 cm respectively. If it is cut into exact number of equal cubes, then find the least possible number of cubes. 
1. 26187
2. 21187
3. 28287
4. 21687

Answer 1

Correct Answer - Option 1 : 26187

Given:
Length of a box = 84 cm
Breadth of a box = 116 cm
Height of a box = 172 cm

Concept used:
Volume of cuboid = l × b × h
Volume of cube = (Side)³
Number of cubes formed from large cuboid = Volume of cuboid/Volume of cube

Calculation:
Volume of cuboid = 84 × 116 × 172
H.C.F of 84, 116 and 172 = 4
The least side of the cube = 4 cm
Volume of cube = 4³
Number of cubes formed = (84 × 116 × 172)/(4 × 4 × 4)
⇒ 21 × 29 × 43
⇒ 26187
∴ The least number of cubes formed would be 26187.