Question 51
Lucia wants to write three positive integers $a, b, c$ such that each of them is a divisor of $30$ and the greatest common divisors of two consecutive terms (that is, $\operatorname{gcd}(a, b)$ and $\operatorname{gcd}(b, c)$) are prime numbers. In how many ways can she do this?
(A) 69
(B) 72
(C) 105
(D) $2^{7}$
(E) None of the above.
(A) 69
(B) 72
(C) 105
(D) $2^{7}$
(E) None of the above.