Question

How many 3 digit positive integers N are there, such that N is a multiple of both 7 and 13?

Answer 1

If the number is a multiple of both 7 and 13, it must be a multiple of 91. So find the multiples of 91 between 100 and 1000.

Answer 2

100<91n<1000
1<n<11

Answer 3

as both 7 1nd 13 are primes
the required number is [1000/91] -1 (as 91 itself is less than 100) =10 -1 =9