Find four consecutive even numbers...

Question

...such that the smallest is a multiple of 5, the second a multiple of 7, the third a multiple of 9, and the largest a multiple of 11.

Answer 1

3740=5*694

3742=7*496

3744=9*386

3746=11*316

So, the numbers are:

{3470, 3472, 3474, 3476},

But for now I couldn't prove that there is no smaller numbers.