6. Let $1 \leqslant a \leqslant b \leqslant 100$, and $57 \mid a b$. The number of positive integer pairs $(a, b)$ is ( ).
(A) 225
(B) 228
(C) $\overline{231}$
(D) 234
6.B.

Obviously, $57=3 \times 19$.
We proceed with the classification and counting.
(1) If $57 \mid a$, then $a=57, b=57,58, \cdots, 100$, i.e., there are $100-56=44$ pairs $(a, b)$.
(2) If $57 \mid b$, and $57 \nmid a$, then $b=57, a=1,2, \cdots, 56$, i.e., there are 56 pairs $(a, b)$.
(3) If $3 \mid a, 19 \mid b$, and $a \neq 57, b \neq 57$, then $a=3x$, $b=19y$, where $x, y$ are positive integers, and $3x \leqslant 19y \leqslant 100, x \neq 19$, $y \neq 3$, i.e.,
$$
\left\{\begin{array}{l}
y=1,2,4,5, \\
x \neq 19, \\
1 \leqslant x \leqslant\left[\frac{19}{3} y\right] .
\end{array}\right.
$$

Thus, the number of pairs $(a, b)$ is the number of pairs $(x, y)$
$$
=6+12+(25-1)+(31-1)=72.
$$
(4) If $19 \mid a, 3 \mid b$, and $a \neq 57, b \neq 57$, then $a=19x$, $b=3y$, and $19x \leqslant 3y \leqslant 100, x \neq 3, y \neq 19$, where $x, y$ are positive integers, i.e.,
$$
\left\{\begin{array}{l}
x=1,2,4,5, \\
y \neq 19, \\
1+\left[\frac{19}{3} x\right] \leqslant y \leqslant 33 .
\end{array}\right.
$$

Thus, the number of pairs $(a, b)$ is the number of pairs $(x, y)$
$$
\begin{aligned}
= & (33-6-1)+(33-12-1)+(33-25) \\
& +(33-31) \\
= & 56 .
\end{aligned}
$$

In summary, the number of positive integer pairs $(a, b)$ that satisfy the conditions is
$$
44+56+72+56=228.
$$