Find the number of numbers lying between 1 and 1,00,000 which are divisible by each of 15,35 and 77 and are even also .

Explanation

The required number must be the multiples of the LCM of 15, 35 and 77. Now the LCM of 15, 35 and 77 = 1155. So the other numbers are 1155, 2310, 3465, 4620, 5775, ..... , 99330. Thus there are total 86 numbers which are divisible by 15, 35 and 77 but only 43 numbers are even i.e. every alternate number is even. Thus there are total 43 required numbers.