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Problem 652

AMC 10/12, early questions

Geometry Difficulty 3.0 Find the answer CEMC Pascal · Canada · 2002

A rectangular block, with dimensions 4 cm, 5 cm and 6 cm, is made up of cubes each with side length 1 cm. If $1\text{ cm}^3$ cubes are removed from this larger rectangular block, what is the minimum number of these cubes that must be removed so that the resulting solid is itself a cube? (A) $40$ (B) $93$ (C) $46$ (D) $64$ (E) $56$

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