How many ordered pairs of positive integers $(m,n)$ satisfy $\gcd(m,n) = 2$ and $\mathop{\text{lcm}}[m,n] = 108$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
How many ordered pairs of positive integers $(m,n)$ satisfy $\gcd(m,n) = 2$ and $\mathop{\text{lcm}}[m,n] = 108$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
How many ordered pairs of positive integers $(m,n)$ satisfy $\gcd(m,n) = 2$ and $\mathop{\text{lcm}}[m,n] = 108$?
train