1. **State the problem:** We need to find how often tours for the National Capitol and the White House leave at the same time, given that National Capitol tours leave every 15 minutes and White House tours leave every 20 minutes, starting at 8:30 A.M. 2. **Identify the formula:** This is a problem of finding the Least Common Multiple (LCM) of the two intervals (15 and 20 minutes) because the tours will leave together at multiples of both intervals. 3. **Find the prime factorizations:** - 15 = $3 \times 5$ - 20 = $2^2 \times 5$ 4. **Calculate the LCM:** The LCM is found by taking the highest powers of all prime factors: $$\text{LCM} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60$$ 5. **Interpret the result:** The tours leave at the same time every 60 minutes. 6. **Final answer:** The tours leave together every $60$ minutes, or every 1 hour, starting from 8:30 A.M.