Let $\rm (a,b)=d,a=da_1,b=db_1,lcm(a,b)=da_1b_1$ We have that $\rm d^2a_1b_1+63=20da_1b_1+12d\Rightarrow d\mid 63\Leftrightarrow d=1,3,7,9,21,63 $ Also $\rm 63-12d=a_1b_1d(20-d)\Rightarrow 20-d\mid 63-12d\Leftrightarrow 20-d\mid (20-d)12-(63-12d)=177$. $\rm 20-1\not |177,20-3\not |177,20-7\not | 177,20-9\not | 177,20-21\mid 177,20-63\not | 177$ so $\rm d=21$. Therefore $\rm 441a_1b_1+63=420a_1b_1+252\Leftrightarrow 21a_1b_1=189\Leftrightarrow a_1b_1=9$. Since $\rm (a_1,b_1)=1$ we have $\rm a_1=1,b_1=9\,\,or\,\,\,a_1=9,b_1=1$. $\rm a_1=1,b_1=9\Leftrightarrow \boxed {\rm (a,b)=(21,189),(189,21)}$.