Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability / 2 / a / Solution

Use the inclusion-exclusion principle on the multiples of $6,8,11$ in $\{1,\dots ,527\}$. The pairwise least common multiples are $24,66,88$, and the triple least common multiple is $264$. Therefore the count isThe endpoint $528$ is excluded, which is why the numerators are $527$ rather than $528$.