6. The sequence of positive integers $\left\{a_{n}\right\}: a_{n}=3 n+2$ and $\left\{b_{n}\right\}: b_{n}=5 n+3, n \in \mathbf{N}$, have a certain number of common terms in $M=\{1,2, \cdots, 2018\}$. Find the number of these common terms.
荅建 135.
解析 设公共项构成的数列为 $\left\{c_{n}\right\}$, 则 $\left\{c_{n}\right\}$ 是首项为 8 , 公差 $d=15$ 的等差数列, 2018 是 $\left\{c_{n}\right\}$ 的最后一项, 所以 $c_{n}=8+15(n-1)=2018$, 解得 $n=135$.

Translation:
Answer 135.
Analysis: Let the sequence formed by the common terms be $\left\{c_{n}\right\}$. Then $\left\{c_{n}\right\}$ is an arithmetic sequence with the first term 8 and common difference $d=15$. The last term of $\left\{c_{n}\right\}$ is 2018, so $c_{n}=8+15(n-1)=2018$, solving for $n$ gives $n=135$.