#1**0 **

Start with numbers divisible by 16. The smallest number is 16 (16 x 1), and the largest number is 4000 (16 x 250). This makes for 250 integers.

Now, we do the numbers divisible by 30. The smallest number is 30 (30 x 1), and the largest is 3990 (30 x 133). This makes for 133 integers.

However, we double count for every multiple of 240 (lcm of 16 and 30). The smallest number we overcount for is 240 (240 x 1) and the largest is 2840 (240 x 16). This makes for 16 integers.

Thus, there are \(250 + 133 - 16 = \color{brown}\boxed{367}\) integers.

BuilderBoi Jun 29, 2022