Question

If both 52 and 33 are factors of n x 25 x 62 x 73, what is the smallest possible positive value of n?

• A. 45
• B. 27
• C. 25
• D. 75

Answer 1

Answer: (D)

75

Answer 2

$(2^5)\times(6^2)\times(7^3)\times n$ is the given number.
If both $5^2,3^3$ are factors, then they must be present in the number.
Leaving rest of the prime factors and splitting $6^2$ into $3^2\times2^3$.
The number is lacking $5^2$ and a3, so that $5^2$ and $3^3$ is a factor.
Hence the smallest number is $5^2\times3=75$
The correct option is (D): 75