8. How many pairs of positive integers $(a, b)$, with $a<b$, are there such that $\operatorname{gcd}(a, b)=2$ and $\operatorname{lcm}(a, b)=60$?
(A) 0
(B) 4
(C) 3
(D) 2
(E) 6
(8) The correct answer is $(B)$.

The product of $a$ and $b$ is $120=2^{3} \cdot 3 \cdot 5$. Since $M C D(a, b)=2$, one of the two numbers will have only one factor of 2 in its factorization, while the other will have two; the other prime factors 3 and 5 are present in the product $a b$ only once, and will therefore not contribute to the $M C D$. The pairs of integers obtained are then:

$$
(2,60), \quad(6,20), \quad(10,12), \quad(4,30) \text {. }
$$

Problem proposed by Antonio Fanelli and Riccardo Zanotto.