Question

what is the smallest number by which 17496 may be multiplied so that the product is a perfect cube

Answer 1

Using prime factorization of 17496

17496 = 2×2×2×3×3×3×3×3×3×3

So the smallest number is 3×3 = 9

Hence the smallest number 9 multiplied to 17496 so that the product is a perfect cube.