Answer :
To Find :
How many of the smallest 200 positive integers are divisible by 3,5 and 7 .
Solution :
We have to find number which are divisible by all 3,5 and 7 .
So , we will find numbers which are divisible by their H.C.F .
Since , 3 ,5 and 7 are prime numbers .
Therefore , their H.C.F is [tex]3\times 5\times 7=105[/tex] .
Now , we can see that HCF is 105 , so the next number which is divisible by all of them are [tex]105\times 2=210[/tex] which is greater than 200 .
Therefore , their is only 1 number i.e 105 less than 200 which is divisible by 3,5 and 7 .
Hence , this is the required solution .
