= Solution
Use the <inclusion-exclusion principle> on the multiples of $6,8,11$ in $\{1,\ldots,527\}$. The pairwise <least common multiples> are $24,66,88$, and the triple <least common multiple> is $264$. Therefore the count is
$$
\begin{aligned}
&\left\lfloor\frac{527}6\right\rfloor+
\left\lfloor\frac{527}8\right\rfloor+
\left\lfloor\frac{527}{11}\right\rfloor-
\left\lfloor\frac{527}{24}\right\rfloor-
\left\lfloor\frac{527}{66}\right\rfloor-
\left\lfloor\frac{527}{88}\right\rfloor+
\left\lfloor\frac{527}{264}\right\rfloor\\
&=87+65+47-21-7-5+2=\boxed{167}.
\end{aligned}
$$
The endpoint $528$ is excluded, which is why the numerators are $527$ rather than $528$.
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