Discussion
A rectangular block 6 cm × 12 cm × 15 cm is cut into exact number of equal cubes. The least possible number of cubes will be
Answer: D
The cubes must fit a whole number of times along each edge, so their edge length must divide 6, 12 and 15. To make the fewest cubes, take the largest such edge - the highest common factor.
\[ \text{HCF}(6, 12, 15) = 3 \]
\[ n = \frac{6}{3} \times \frac{12}{3} \times \frac{15}{3} = 2 \times 4 \times 5 = 40 \]
Equivalently \( \tfrac{6 \times 12 \times 15}{3^{3}} = \tfrac{1080}{27} = 40 \). Fewest cubes means largest cubes - the two requirements pull in opposite directions.
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