Let A be the set of positive integers that have no prime factors other than 2,3 , or 5 . The infinite sum
\dfrac{1}{1}+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{16}+\dfrac{1}{18}+\dfrac{1}{20}+\cdots
of the reciprocals of all the elements of A can be expressed as \dfrac{m}{n}, where m and n are relatively prime positive integers. What is m+n ?
Answer Choices
A. 16
B. 17
C. 19
D. 23
E. 36