At a local store, hot dogs come in packages of 8, and hot dog buns come in packages of 12. For her party, Arpitha purchased the minimum number of hot dog packages and bun packages that she could while making sure to have the same number of hot dogs and buns. How many hot dogs can Arpitha serve at her party?
A: 4
B: 24
C: 48
D: 96
the answer is 24
To find out how many hot dogs Arpitha can serve at her party, we need to determine the least common multiple (LCM) of 8 and 12, which represents the minimum number of hot dogs and buns that can be purchased.
To find the LCM, we can list the multiples of each number until we find a common multiple:
Multiples of 8: 8, 16, 24, 32, 40, 48, ...
Multiples of 12: 12, 24, 36, 48, 60, ...
From the list above, we can see that the LCM of 8 and 12 is 24.
Since Arpitha wants to have the same number of hot dogs and buns, she will need to purchase 24 hot dogs, which is the LCM.
Therefore, the answer is B: 24.