Problem Solving

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?

Also, please explain me the solution

lets expand n x (2^5) x (6^2) x (7^3) and this can written as
= nx (2^5)x(7^3)x(2^2x3^2)
now as we can see that 5^2 is completely missing from the expression above
so n must atleast have 5^2
and we can also infer from the expression that in order for 3^3 to be factor of the expression
we would need one more 3 as 3^2 is already present
this means

n = 5*5*3 = 75
Is this the answer?

indiantiger wrote:lets expand n x (2^5) x (6^2) x (7^3) and this can written as
= nx (2^5)x(7^3)x(2^2x3^2)
now as we can see that 5^2 is completely missing from the expression above
so n must atleast have 5^2
and we can also infer from the expression that in order for 3^3 to be factor of the expression
we would need one more 3 as 3^2 is already present
this means

n = 5*5*3 = 75
Is this the answer?

Yes you are right, answer is 75