There are 3 digit numbers that are each divisible by 7 and by 8 without a remainder in each case. what is the largest of these 3 digit numbers?

To be divisible by both 7 and 8 a number must be a multiple of 56.

Multiples of 56 are just 56n. We wish to know the largest of three digit numbers that is a multiple of 56 then. So:

56n<1000

n<1000/56

n<17.86 and since n must be an integer n=17

Then the largest three digit multiple of 56 is:

56 (17) = 952