A rectangular block with sides 6 cm, 12 cm and 15 cm is cut up into an exact number of equal cubes. The least possible number of cubes is?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 40
The fewest cubes means the largest possible cube. Its side must divide each of 6, 12 and 15 with no remainder, so the largest side is the HCF of the three lengths.
HCF of 6, 12 and 15 = 3, so each cube has side 3 cm
Cubes along the three edges: \(\frac{6}{3}=2\), \(\frac{12}{3}=4\), \(\frac{15}{3}=5\)
Number of cubes: \(2\times4\times5=40\)