Let n be the least positive integer such that 1260n is the cube of a natural number. then n satisfies?

Question

a) 1 b) 50 c) 100 d) 1000

Answer 1

Prime factorize 1260 first, you get 1260 = 2^2 * 3^2 * 5 * 7, so to "complete the cube", all the exponents must be a multiple of 3. So n has one 2, one 3, two fives, and two seven. So n=7350, the answer is D.

Answer 2

Let's factor 1260 first.
We get 2²*3²*5*7.
To make a cube of 1260n, we want the exponents
of each of these prime factors to be a multiple of 3.
So we must take n = 2*3*5²*7² = 150*49 = 7350.
Answer is d).

Answer 3

answer is (d)