4 packages of buns, and 5 packages of chicken patties.
Step-by-step explanation:
8 = 2 X 2 X 2
10 = 5 X 2
The Least Common Multiple of 8 and 10 = 2 X 2 X 2 X 5 = 40, now divide 40/10 = 4 and 40/8 =5 therfore you need to buy: 4 packages of buns, and 5 packages of chicken patties.