Question

Find the least number must be multiplied with 3456such that tht product becomes a perfect cube

Answer 1

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

= 2^7 * 3^3.
=(3*2*2*2)*(3*2*2*2)*(3*2)
=24*24*6

For 6 to become 24 ,it should be multiplied with 4 so that no. is perfect cube
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 .
=24^3