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 thee white house leave every 20 minutes how often do the tours leave at the same time
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 of 15 and 20 is 60.
Therefore, the tours 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 need to find the least common multiple (LCM) of 15 minutes and 20 minutes.
The LCM is the smallest positive integer that both 15 and 20 divide into evenly.
We can find the LCM using the prime factorization method:
Prime factors for 15: 3 * 5
Prime factors for 20: 2^2 * 5
Now, we take the highest power of each prime factor from both numbers:
Highest power of 2: 2^2 = 4
Highest power of 3: 3^1 = 3
Highest power of 5: 5^1 = 5
Multiplying these highest powers together, we get:
4 * 3 * 5 = 60
Therefore, the tours for 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 time intervals at which the tours overlap.
The tour of the national Capitol leaves every 15 minutes, and the tour of the White House leaves every 20 minutes. To find the least common multiple (LCM) of these two intervals, we can multiply them and then divide by their greatest common divisor (GCD).
Step 1: Find the GCD of 15 and 20.
- The factors of 15 are 1, 3, 5, 15.
- The factors of 20 are 1, 2, 4, 5, 10, 20.
The greatest common divisor (GCD) is 5.
Step 2: Calculate the LCM using the GCD.
LCM = (15 * 20) / GCD = 300 / 5 = 60 minutes.
Therefore, the tours of the National Capitol and the White House will leave at the same time interval of 60 minutes.