The school cafeteria serves tacos every sixth day and cheeseburgers every eight day. If tacos and cheeseburgers are served on the same day, how many days will it be before they are both on the menu again.
What is the least common multiple of 6 and 8?
24
To find the number of days before tacos and cheeseburgers are both on the menu again, we need to determine the least common multiple (LCM) of 6 and 8.
First, let's list the dates on which tacos are served:
Day 1: Tacos
Day 2:
Day 3:
Day 4:
Day 5:
Day 6: Tacos
Now, let's list the dates on which cheeseburgers are served:
Day 1:
Day 2:
Day 3:
Day 4:
Day 5:
Day 6:
Day 7:
Day 8: Cheeseburgers
As we can see, the first time both tacos and cheeseburgers are on the menu is on Day 6 and Day 8.
To find the LCM of 6 and 8, we can list the multiples of 6 and 8 until we find a common multiple:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ...
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
From the lists, we can see that 24 is the smallest common multiple of 6 and 8.
Therefore, it will take 24 days for tacos and cheeseburgers to both be on the menu again.
To solve this problem, we need to find the least common multiple (LCM) of 6 and 8, which will give us the number of days before tacos and cheeseburgers are both on the menu again.
Step 1: Find the multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ...
Step 2: Find the multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
Step 3: Identify the common multiple in both lists. The common multiple is 24.
Therefore, tacos and cheeseburgers will both be on the menu again in 24 days.