3. Determine all seven-digit numbers of the form $\overline{2016 a b c}$ that are divisible by 5, 7, and 13.
First method:

Since 5, 7, and 13 are prime numbers, they are relatively prime in pairs, so the desired number must be divisible by $5 \cdot 7 \cdot 13 = 455$.

3 POINTS

Since $2016000 = 4430 \cdot 455 + 350$,

1 POINT

the desired numbers are $4431 \cdot 455 = 2016105$

1 POINT

and $4432 \cdot 455 = 2016560$.

1 POINT

TOTAL 6 POINTS

Note: 1 point is awarded for the conclusion that the desired number must be divisible by the least common multiple of the numbers 5, 7, and 13, even if this multiple is not determined or is not correctly determined.

An unexplained conclusion that the desired number must be divisible by $5 \cdot 7 \cdot 13 = 455$ (if it is not explained that $\mathrm{V}(5,7) = 35$ and $\mathrm{V}(35,13) = 455$, or that $\mathrm{V}(5,7,13) = 455$ based on the fact that the numbers 5, 7, and 13 are relatively prime) earns only 1 point.