Let's see how good /prog/ really is

Can you find the smallest number that fulfills the following criteria?

1. It can only contain digits of 3, 5 and 7
2. The sum of the digits can be divided by 3, 5 and 7 without remainder
3. The number can be divided by 3, 5 and 7 without remainder

>>5
That's nowhere near the answer, I bet. This does sound like it's real easy to bruteforce, though.

Some ideas:

- The last digit is a 5.
- The number is an odd multiple of 105.
- The number's digit sum is a multiple of 105.