A box measuring 90 inches long by 45 inches wide by 9 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? Choose the correct choice from the following answers:
A) 17  B) 18  C) 50  D) 108  E) 864
least number of cubes will be required when the cubes that could fit in are biggest.   9 is the biggest number that could divide all three, 90, 45 and 9.   Thus side of cube must be 9, and total number of cubes = 90/9 * 45/9*9/9= 
<gadget id="calculator">90/9 * 45/9*9/9</gadget>
<output>50</output>
50   Ans 50 it is.
<result>C</result>
A box measuring 90 inches long by 45 inches wide by 9 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?