A box measuring 72 inches long by 48 inches wide by 24 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective? Answers:
A) 17 B) 18 C) 54 D) 108 E) 162
least number of cubes will be required when the cubes that could fit in are biggest.   8 is the biggest number that could divide all three, 72, 48 and 24.   Thus side of cube must be 8, and total number of cubes = 72/8 * 48/8*24/8= 
<gadget id="calculator">72/8 * 48/8*24/8</gadget>
<output>162</output>
162   Ans 162 it is.
<result>E</result>
A box measuring 72 inches long by 48 inches wide by 24 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?