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 60 minutes every 60 minutes every 15 minutes every 15 minutes every 30 minutes every 30 minutes every 35 minutes
To find 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 multiples of 15 minutes are: 15, 30, 45, 60, ...
The multiples of 20 minutes are: 20, 40, 60, ...
The LCM is the smallest number that appears in both lists. In this case, the LCM is 60 minutes. 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 the intervals at which the tours leave.
The interval for tours of the National Capitol is 15 minutes, and the interval for tours of the White House is 20 minutes.
The LCM of 15 and 20 is 60 minutes.
Therefore, the tours of the National Capitol and the White House 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 the intervals at which the tours leave. In this case, the tours of the National Capitol leave every 15 minutes, and the tours of the White House leave every 20 minutes.
To find the LCM, we need to identify the smallest multiple that both 15 and 20 divide evenly into. We can do this by finding the prime factors of each number:
15 = 3 * 5
20 = 2^2 * 5
To determine the LCM, we take the highest power of each prime factor that appears in either number:
LCM = 2^2 * 3 * 5 = 60.
Therefore, the tours will leave at the same time every 60 minutes. Thus, the correct response is: every 60 minutes.