Let $F_n$ denote the $n$-th Fibonacci number: $F_1=1, F_2=1, F_3=2, F_4=3, F_5=5, F_6=8, F_7=13, F_8=21, F_9=34, F_{10}=55, F_{11}=89, F_{12}=144$. What is $\gcd(F_8, F_{12})$?