Question

Find the no of integers between 1and250 both are divisible by 2,3,5,7 integer

Answer 1

I will first consider all integers up to 210210, as it is the L.C.M. of 22, 33, 55 and 77. The number of integers from 11 to 210210 which are not divisible by 22, 33, 55 or 77 is

210−2102−2103−2105−2107+2106+21010+21014+21015+21021+21035−21030−21042−21070−210105+210210210−2102−2103−2105−2107+2106+21010+21014+21015+21021+21035−21030−21042−21070−210105+210210

which is equal to

210(1−12)(1−13)(1−15)(1−17)=48210(1−12)(1−13)(1−15)(1−17)=48

The integers from 211211 to 250250 can be replaced by 11 to 4040. I prefer to simply list out all integers satisfying the conditions: 11, 1111, 1313, 1717, 1919, 2323, 2929, 3131, 3737.

So, there are 48+9=5748+9=57 such integers

I hope this will help you

Answer 2

heya..

Yes. .they are all integers