Question

Find the smallest number by which 12348 be multiplied so that it becomes a perfect cube

Answer 1

12348
= 2 x 2 x 3 x 3 x 7 x 7 x 7

Therefore required number
= 2 x 3
= 6


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Answer 2

Solution:-
12348=2×2×3×3×7×7×7

Here,we can see that prime factor 7 is in group of three but 2 and 3 are not in group of three.

Only the number whose prime factor are in group of three can be perfect cube.

Here,we have to make 2 and 3 in group of three.For this we will have to multiple the number by2×3=6.

Hence,the number which should be multiplied to 12348 to make it perfect cube is 6.