7. (10 points) For a natural number $N$, if at least six of the nine natural numbers from $1$ to $9$ can divide $N$, then $N$ is called a "Six-Union Number". The smallest "Six-Union Number" greater than 2000 is $\qquad$ .
【Solution】Solution: According to the problem, we have:
To satisfy being a hexagonal number. It is divided into being a multiple of 3 and not being a multiple of 3.
If it is not a multiple of 3, then it must be a multiple of $1,2,4,8,5,7$, so their least common multiple is: 8 $\times 5 \times 7=280$. Then the smallest number greater than 2000 that is a multiple of 280 is 2240.

If it is a multiple of 3. It must also satisfy being a multiple of $1,2,3,6$. It needs to satisfy 2 more numbers.
The smallest number greater than 2000 is 2004 (a multiple of 1, 2, 3, 4, 6) which does not meet the requirement;
2010 is (a multiple of 1, 2, 3, 5, 6) which does not meet the requirement;
2016 is (a multiple of $1,2,3,4,6,7,8,9$) which meets the requirement.
$2016<2240$;
Therefore, the answer is: 2016