3. How many three-digit positive numbers $x$ exist that are divisible by 3 and satisfy the equation $GCD(15, GCD(x, 20))=5$? Find the largest one.
3. Solution. Since 20 is not divisible by 3, $NOD(x, 20)$ is also not divisible by 3. Therefore, the equation $NOD(15, NOD(x, 20))=5$ is equivalent to the condition that $NOD(x, 20)$ is divisible by 5, which is possible if and only if $x$ is divisible by 5. Thus, the condition of the problem is equivalent to $x$ being divisible by 5 and by 3, that is, $x$ is divisible by 15. Therefore, $x$ can be written as $x=15m, m=1,2 \ldots$. The smallest three-digit $x=105$ is obtained when $m=7$, and the largest three-digit $x=990$ is obtained when $m=66$, making a total of 60 numbers.