29-30 Let $a, b$ be positive integers $(a>b)$, $p$ is the greatest common divisor of $a, b$, and $q$ is the least common multiple of $a, b$. Then the size relationship of $p, q, a, b$ is
(A) $p \geqslant q \geqslant a>b$.
(B) $q \geqslant a>b \geqslant p$.
(C) $q \geqslant p \geqslant a>b$.
(D) $p \geqslant a>b \geqslant q$.
(2nd "Hope Cup" National Mathematics Invitational Competition, 1991)
[Solution] From the given, we know that $p \leqslant \min \{a, b\}$, and $q \geqslant \max \{a, b\}$, thus
$$
p \leqslant b < a \leqslant q .
$$

Therefore, the correct choice is $(B)$.