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Q.

What is the smallest number by which 68600 must be multiplied to get a perfect cube?


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a

4

b

5

c

6

d

7 

answer is B.

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Detailed Solution

It is required to find the smallest number by which 68600 must be multiplied to get a perfect cube.
Utilizing prime factorization, express the given integer as a prime factor product.
68600=2×2×2×5×5×7×7×7= 2 3 × 5 2 × 7 3  
68600 is not a perfect cube since factor 5 does not contain triples.
The result of multiplying 68600 by 5 is a number that forms a perfect cube.
Therefore, 5 is the least number that needs to be multiplied to 68600 to produce a perfect cube.
Hence, option 2 is correct.
 
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