Suppose $A,B$,and $C$ are integers greater than or equal to $2$. If $\gcd(A,B)=12, \text{lcm}(A,B)=396$ and $\gcd(B,C)= 33$,what is the $\gcd(11A,B)$?

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Suppose $A,B$,and $C$ are integers greater than or equal to $2$. If $\gcd(A,B)=12, \text{lcm}(A,B)=396$ and $\gcd(B,C)= 33$,what is the $\gcd(11A,B)$?

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