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?

Question

Mathematics

Araceli Shea

12 May, 00:47

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?

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Answers (1)

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Jaxon Acosta · Answer 1

24

Step-by-step 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.