Anthony denotes in sequence all positive integers divisible by $2$. Bertha denotes in sequence all positive integers divisible by $3$. Claire denotes in sequence all positive integers divisible by $4$. Orderly Dora denotes all numbers written by the other three. She puts them in order by size and does not repeat a number. What is the $2017^{th}$ number in her list?

Let's think step by step and output the final answer within \boxed{}.
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