7. Find the smallest six-digit number that is divisible by 3, 7, and 13 without a remainder.
7. The desired number must be divisible by $3 \cdot 7 \cdot 13=273$, and the smallest six-digit number $100000=366 \cdot 273+82$. If we add 191 to it, we get $100191=367 \cdot 273$. This is the desired number.