Question

the least number must be multiplied with 3456 such that the product become a perfect cube

Answer 1

Prime factorization of 3456 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3

                                               = 2^7 * 3^3.


The number 2 should be multiplied twice so that the product is a perfect cube.

Therefore the smallest number by which 3456 must be multiplied = 2 * 2 * 

                                                                                                               = 4.

3456 * 4 = 13824

               = 24 * 24 * 24 .


Hope this helps!

Answer 2

first find prime factors of 3456

3456=2×1728

=2×2×864

=2×2×2×432

=2×2×2×2×216

=2×2×2×2×2×108

=2×2×2×2×2×2×54

=2×2×2×2×2×2×2×27

=2×2×2×2×2×2×2×3×3×3

Take 3 same numbers and by remaining number the number should be multiplied to get perfect cube

means here 3456 is multiplied by 2 to get perfect square