Beginning at 8:30am, tours of the National Capitol and the White House begin. Tours for the National Capitol leave every 10 minutes. Tours for the White House leave every 15 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 10 and 15 minutes, as that will be the interval at which the tours coincide.
The prime factorization of 10 is 2 * 5,
The prime factorization of 15 is 3 * 5.
The LCM is found by multiplying the highest power of each prime factor:
LCM = 2 * 3 * 5 = 30 minutes.
Therefore, the tours leave at the same time every 30 minutes.