Step 1 :\text{Find the least common multiple of 7 and 9: } \text{lcm}(7, 9) = 63
Step 2 :\text{Calculate packs of hot dogs: } \frac{63}{7} = 9 \text{ packs}
Step 3 :\text{Calculate packs of buns: } \frac{63}{9} = 7 \text{ packs}
Step 4 :\text{Find the total number of hot dogs: } 9 \times 7 = 63 \text{ hot dogs}