Find the least common multiple of 12 and 9:
9, 18, 27, 36, 45, 54
12, 24, 36, 48, 60
The smallest number ( least common multiple) for both 9 and 12 is 36.
This means she needs to buy 36 hot dogs and rolls, which would be 4 packages of hot dogs and 3 packages of hot dog rolls.