There are exactly 77,000 ordered quadruples (a, b, c, d) such that \operatorname{gcd}(a, b, c, d)= 77 and \operatorname{lcm}(a, b, c, d)=n. What is the smallest possible value of n ?
Answer Choices
A. 13,860
B. 20,790
C. 21,560
D. 27,720
E. 41,580