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?
*
1 point
Every 1 ½ hours
Every 30 minutes
Every hour
They never 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 10 and 15.
The prime factors of 10 are 2 and 5, while the prime factors of 15 are 3 and 5.
To find the LCM, we take the highest power of each prime factor that appears in either number:
2^1 * 3^1 * 5^1 = 2 * 3 * 5 = 30
Therefore, the tours for the National Capitol and the White House leave at the same time every 30 minutes.