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
