a box measuring 49 inches long by 21 inches wide by 14 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?
Options.
A) 17
B) 42
C) 54
D) 108
E) 864
<gadget id="calculator">49 * 21</gadget>
<output>1_029</output>

<gadget id="calculator">1_029 * 14</gadget>
<output>14_406</output>

<gadget id="calculator">14 / 2</gadget>
<output>7</output>

<gadget id="calculator">7 ** 3</gadget>
<output>343</output>

<gadget id="calculator">14_406 / 343</gadget>
<output>42</output>

<result>B</result>
a box measuring 49 inches long by 21 inches wide by 14 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?
divide(multiply(multiply(49, 21), 14), volume_cube(divide(14, const_2)))
"least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 21 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 21 / 7 * 14 / 7 = 42 ans b it is ."