Explanation:
To find the smallest total number of hot dogs that Yadira's mom can purchase, we need to find the least common multiple (LCM) of 12 and 9, since she wants the same number of hot dogs as hot dog buns.
The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...
The least common multiple of 12 and 9 is 36, since it is the smallest number that appears in both lists. Therefore, Yadira's mom should purchase 36 hot dogs (3 packs of 12) and 36 hot dog buns (4 packs of 9) for the family barbecue.