Thread: Multiples of 2, 3, 5, but not 7

Instead of writing all of the multiples out by hand, what is the easiest way to find how many integers from 200 to 500 that are multiples of 2,3,5 but not 7?

240 270 300 330 360 390 450 480

Just to clarify, did you mean divisible by 2, 3, AND 5, but NOT 7 ? If so, just find the LCM of 2, 3, and 5, which is 30. Search for numbers divisible by 30 but not 210 (LCM of 30, 7).

If you only need to know the number of numbers which satisfy both of those rules then you can try the following:
Hi.
If a number is divisible by 2,3,5 ,then its divisible by 30 .
For example , to find the numbers smaller that 200 that are divisible by 30 , just divide 200 by 30 .
200 : 30 = 6
So there are 6 numbers that are simultaneously divisibler by 2,3,5.
Similary , if you don't want a number to be divisible by another number , just eliminate possible cases:

Q: Find number of integer divisible by 3 ,not divisible by 5 between 1 and 21.
21/2=7 (7 numbers are divisible by 3)
21/10=1 ( 1 number is divisible by both 3 and 5)
7-1=6 numbers are divisible by 3 but not divisible by 5. (This result can be shown by simple properties of sets)