Factored 'n'

Number Theory Level 2

$\text{If both}$ $5^2$ and $3^3$ are factors of $n (2^5) (6^2) (7^3)$ , what is the smallest possible value of $n$ ?

2 solutions

Mohit Gupta
Aug 12, 2015

See its pretty easy you just need to concentrate on that 6^2=2^2×3^2

Anish Harsha
Aug 12, 2015

$n (2^5)(6^2)(7^3)$ should be divisible by $5^2$ and $3^3$ .
Then, the minimum value of $n$ is $5^2 \times 3 = 75$
So, the answer is 75.