L.C.M. and ordered pairs

If the number of ordered pairs of positive integers $(a, b)$ such that the least common multiple of $a$ and $b$ is $2^5.5^{11}.11^{17}$ is $A$ , then find the sum of digits of $A$ .

Details and Assumptions

If the value of A is $3456$ , then you enter $3+4+5+6 = 18$ as your answer.

You may use a calculator.