Let $m$ and $n$ be positive integers such that $$\begin{aligned}
& \gcd ( m , n ) + \text{lcm} ( m , n ) = 289 \\
& m + n \neq 289
\end{aligned}$$ What is the sum $m + n$? A) 41 B) 43 C) 45 D) 47 E) 49
Let $m$ and $n$ be positive integers such that
$$\begin{aligned}
& \gcd ( m , n ) + \text{lcm} ( m , n ) = 289 \\
& m + n \neq 289
\end{aligned}$$
What is the sum $m + n$?\\
A) 41\\
B) 43\\
C) 45\\
D) 47\\
E) 49