KöMaL 2013 K399

$a$) How many numbers $A$ are there for which the least common multiple of $6^6$, $8^8$ and $A$ is $12^{12}$? $b$) How many numbers $B$ less than 1000 are there for which the greatest common divisor of $6^6$, $30^3$ and $B$ is $3^3$?