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?
To find out 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 prime factors of 15 are 5 and 3.
The prime factors of 20 are 5, 2, and 2.
Writing out all the prime factors, we get:
15 = 3 * 5
20 = 2 * 2 * 5
To find the LCM, we take the highest power of each factor that appears in either prime factorization:
LCM = 2 * 2 * 3 * 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 prime factors of 15 are 3 and 5.
The prime factors of 20 are 2, 2, and 5.
To find the LCM, we take the highest power of each prime factor that appears in either number:
2^2 × 3 × 5 = 60
Therefore, the tours will leave at the same time every 60 minutes.
To determine how often the tours for the National Capitol and the White House leave at the same time, we can find the least common multiple (LCM) of the times between each tour.
The time between the National Capitol tours is 15 minutes, while the time between the White House tours is 20 minutes.
To find the LCM, we need to find the smallest number that is divisible by both 15 and 20.
The prime factors of 15 are 3 and 5, while the prime factors of 20 are 2, 2, and 5.
To find the LCM, we take the highest power of each prime factor. In this case, we have 2^2, 3, and 5.
Multiplying these together, we get: 2^2 x 3 x 5 = 60.
Therefore, the tours for the National Capitol and the White House leave at the same time every 60 minutes.