The least number of cuboids that make a perfect cube is 2160
The dimensions of the cuboid are represented as:
- Length = 20 cm
- Width = 15 cm
- Height = 9 cm
Start by taking the LCM of the dimensions (i.e. the LCM of 20, 15 and 9)
[tex]20 = 2 \times 2 \times 5[/tex]
[tex]15 = 3 \times 5[/tex]
[tex]9 = 3 \times 3[/tex]
So, the LCM is:
[tex]LCM = 2 \times 2 \times \times 3 \times 3 \times 5[/tex]
[tex]LCM = 180[/tex]
Divide 180 by the dimensions to calculate the least number of cuboids that makes a perfect cube
[tex]n = \frac{LCM}{Length} \times \frac{LCM}{Width} \times \frac{LCM}{Height}[/tex]
This gives
[tex]n = \frac{180}{20} \times \frac{180}{15} \times \frac{180}{9}[/tex]
[tex]n = 9 \times 12 \times 20[/tex]
[tex]n = 2160[/tex]
Hence, the least number of cuboids that make a perfect cube is 2160
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