I am dealing with divisibility problems, such as:
Find the number of positive integers that is divisible by either of 2 or 5 within 1000. In this case, I decide to look at how many integers are divisible by 2 or 5 within 10, that is 6. So we can deduce that there are 600 numbers that could be divided by 2 or 5 within 1000.
But, what if we are trying to find number of positive integers that is divisible by both 3 or 7 within 1000, I found that the number block of '10' cannot work here, and if we try number block of '21', meaning that to find how many number is divisible by 3 or 7 within 21, and then use 1000 divides 21 to see how many blocks are there within 100, that will work. May I know what is the mechanism behind this or is there any general rule for dealing with this type problem?
Thank you so much for you guy's replies