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Q.

What is the smallest multiple of 72 that results in a perfect cube?


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a

2

b

3

c

4

d

5 

answer is B.

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Detailed Solution

The given number is 72.
First, prime factorize the number 72 to create a product, then group the prime factors into cube groups.
⇒72=2×2×2×3×3= 2 3 × 3 2  
Here the factor 3 does not appear in such groupings (triples), so 3 is required to make a perfect cube.
The smallest number by which 72 can be multiplied to get a complete cube is 3.
Therefore, option 2 is correct.
 
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What is the smallest multiple of 72 that results in a perfect cube?