Question

a rectangular box of dimensions 24cm by 36cm by 48cm was fully packed with wooden cubes of the same size. at least how many cubes were there?

Answer 1

24

Explanation:

Find the GCF of 24, 36 and 48.

Prime factorization of:

24: 2*2*2*3

36: 2*2*3*3

48: 2*2*2*2*3

All numbers have at least two 2s and one 3.

2*2*3=12

The cubes must have been 12x12x12 largest size.

(24*36*48)÷(12*12*12)

=(41472)÷(1728)=24

At 12x12x12, 24 cubes would be packed.

There must be at least 24 cubes.