A box measuring 24 inches long by 40 inches wide by 16 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 most appropriate option:  A) 28  B) 30  C) 32  D) 35  E) 37

Rationale: "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 , 24 , 40 and 16 . thus side of cube must be 8 , and total number of cubes = 24 / 8 * 40 / 8 * 16 / 8 = 30 ans b"
Answer: B