jmc

First, we observe that both $4$ and $25$ will divide into the least common multiple. Thus, $100$ will divide into the least common multiple, and so $C=0$.

Also, we notice that $9$ and $11$ divide into the least common multiple. Thus, the sum of the digits must be divisible by $9$: $$2+6+A+7+1+1+4+B+4=25+A+B=27,36$$and the alternating sum of the digits must be divisible by $11$ (the divisibility rule for $11$): $$2-6+A-7+1-1+4-B+4=-3+A-B=0,-11.$$It follows that $A+B=2,11$ and $A-B=3,-8$. Summing the two equations yields that $2A\in \{-6,3,5,14\}$, of which only $2A=14⟹A=7$ works. It follows that $B=4$, and the answer is $\boxed{740}$.