6. Birgit is looking at positive integers $n$ for which $n$ is divisible by $4$, $n+1$ is divisible by 5, and $n+2$ is divisible by 6.

How many such numbers $n$ exist that are less than 2018?
A) 16
B) 17
C) 18
D) 33
E) 34
A6. E) 34 Of these, that $n$ is divisible by $4$, $n+1$ is divisible by $5$, and $n+2$ is divisible by $6$ is equivalent to the condition that $n-4$ is divisible by $4, 5,$ and $6$. We are looking for numbers $n$ for which $n-4$ is divisible by the least common multiple of $4, 5,$ and $6$, which is $60$. We find the numbers

$$
4, 64, 124, 184, \ldots, 1984
$$

where $1984 = 4 + 33 \times 60$. Together, these are 34 numbers.