Problem Solving

Any help in solving this problem would be great:

If both 5^2 and 3^3 are factors of n x 2^5 x 6^2 x 7^3, what is the smallest possible positive value of n

25
27
45
75
125

Thanks,

n x 2^5 x 6^2 x 7^3=k*5^2*3^3..where k is an integer

or n x 2^5 x 2^2x3^2 x 7^3=k*5^2*3^3

so smallest possible value of n is 5^2*3or 75

Ans option D

chdn20 wrote:Any help in solving this problem would be great:

If both 5^2 and 3^3 are factors of n x 2^5 x 6^2 x 7^3, what is the smallest possible positive value of n

25
27
45
75
125

Thanks,

5^2 is a factor of n x 2^5 x 6^2 x 7^3, no 5 is appearing in the split, 5^2 must be hidden as a factor in n, and also that 3^3 is a factor of n x 2^5 x 2^2 × 3^2 x 7^3, only 3^2 is appearing in the split, the left over 3 must be hidden as a factor in n. For the smallest possible positive value of n, we must not supply anything other than 5^2 × 3 to construct the n in question. This n must be [spoiler]25 × 3 = 75.

D in your order[/spoiler]