How many ordered pairs of positive integers $(m,n)$ satisfy $\text{GCD}(m,n) = 3$ and $\text{LCM}(m,n) = 108?$

LCM of 108 and 3 = 108
GCD of 108 and 3 = 3
LCM of 27 and 12 = 108
GCD of 27 and 12 = 3
LCM of 12 and 27 = 108
GCD of 12 and 27 = 3
LCM of 3 and 108 = 108
GCD of 3 and 108 = 3