Beginning at 8:30 am, tours of the National Capitol and the White House begin at a tour agency. Tours for the National Capitol leave every 15 minutes. Tours for the White House leave every 20 minutes. How often do the tours leave at the same time?(1 point)
Responses
every 30 minutes
every 30 minutes
every 15 minutes
every 15 minutes
every 60 minutes
every 60 minutes
every 35 minutes
The tours leave at the same time every 60 minutes.
In order to determine how often the tours leave at the same time, we need to find the least common multiple (LCM) of 15 and 20.
The prime factorization of 15 is 3 x 5. The prime factorization of 20 is 2 x 2 x 5.
The LCM is found by taking the highest power of each prime factor that appears in either number. Thus, the LCM of 15 and 20 is 2 x 2 x 3 x 5 = 60.
Therefore, the tours leave at the same time every 60 minutes.
To determine how often the tours leave at the same time, we need to find the least common multiple (LCM) of 15 minutes and 20 minutes.
The LCM is the smallest positive integer that is divisible by both 15 and 20. To find the LCM, we can list the multiples of each number and find the smallest shared multiple.
Multiples of 15 minutes: 15, 30, 45, 60, 75, 90, ...
Multiples of 20 minutes: 20, 40, 60, 80, 100, ...
From the lists, we can see that the smallest shared multiple is 60 minutes. Therefore, the tours leave at the same time every 60 minutes.
So the correct response is: every 60 minutes.