how can I find all numbers dividable by multiple numbers between two numbers

Question

How can I find all numbers dividable by let's say 5,7,13 that are 2007***

Answer 1

The number must also be divisible by the least common multiple of $5,7,13$, which is just their product. Now write $2017{*}{*}{*}=2017000+x$ with $0\le x\le 999$, and compute the remainder of division by $5\cdot7\cdot 13$.