Question

4. The smallest positive integer k such that
(2000) (2001) k is a perfect cube!​

Answer 1

Answer:

k = 16016004

Step-by-step explanation:

Factorize (2000)(2001)

(2 x 10 x 10 x 10)(3 x 667)

2 x 3 x 10 x 10 x 10 x 667

The smallest cube including all the same factors is

2 x 2 x 2 x 3 x 3 x 3 x 10 x 10 x 10 x 667 x 667 x 667

thus

k = 2 x 2 x 3 x 3 x 667 x 667

k = 16016004