They advance from 5 x 101=505 to 5 x 200=1000.
The multiples of 5 that are also multiples of 6 are multiples of their LCM. The LCM of 5 and 6 is 30, so the question becomes which multiples of 30 are less than 100? The solution is the numbers: 30, 60, 90
Multiples of 5 include 5, 10 and 15. For them to be common, they need to be compared to another set of multiples.
Since 10 is a multiple of 5, all multiples of 10 will also be multiples of 5. Test the theory. 30, 50, 100... All multiples of 10, and also of 5.
20
There are an infinite number of multiples of 100. 100, 200, 300,400, ....
6 of them.
20,40,60,80,and 100
5,10,15,20,25,30,35,40,45,50,55,60
5, 10, 15 and just keep adding 5 until you get to 100.
100, 200, 300, 400, 500.
100, 200, 300, 400, 500
If 100-300 is inclusive, the answer is 41.