Find the smallest positive integer $k$ such that, for every positive integer $n$, $6n+k$ is relatively prime to each of $6n+3$, $6n+2$, and $6n+1$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the smallest positive integer $k$ such that, for every positive integer $n$, $6n+k$ is relatively prime to each of $6n+3$, $6n+2$, and $6n+1$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
5
Find the smallest positive integer $k$ such that, for every positive integer $n$, $6n+k$ is relatively prime to each of $6n+3$, $6n+2$, and $6n+1$.
train