Question

Find the smallest positive integer k such that 360k is a cube number.

Answer 1

Answer: k = 75

Step-by-step explanation:

                360

                  ∧

             36   10

              ∧     ∧

           6  6   2  5

          ∧    ∧

        2 3  2 3

Prime factorization of 360 is: 2³ · 3² · 5

Since we want a perfect cube, every number must be to the power of 3.

That means we need  a 3 and 2 more 5s  to make a cube

k = 3 × 5 × 5

  = 75

Answer 2

Answer:

k = 75

Step-by-step explanation:

Factorize 360

360 = 36 * 10

      = 2 * 2 * 3 * 3 * 2 * 5

As 360k is cube number, k = 3 * 5 * 5

k = 75

360k = 360 * 75 = 27000 is a perfect cube