Modular arithmetic?

Not really sure how to show work for this one, but I guess you can write out the sets:
First set (N ≡ 3mod7)
N {3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, 80, 87, 94, 101...}

Second set (N≡ 4mod9)
N {4, 13, 22, 31, 40, 49, 58, 67, 76, 85, 94, 103, 112, 121, 130, 149...}

Third set (N ≡ 9mod11)
N {9, 20, 31, ...} Stopped at 31 because it's the first number in each set.

3 mod 7: 3, 10, 17, 24, 31, 38, ...
4 mod 9: 4, 13, 22, 31, 40, ...
9 mod 11: 9, 20, 31, 42, 53, ...

Looks like 31 is the smallest such number.