Question: Trains on two different routes stop at the same train station. Trains on one route stop there every $9$ minutes and trains on the other route stop there every $6$ minutes. Trains on both routes stop at the train station at midday. How many minutes later will it be when trains on both routes next stop there at the same time?

1. **State the problem:** We need to find the time in minutes after midday when trains on both routes will stop at the station simultaneously again. 2. **Identify the key information:** - One train stops every $9$ minutes. - The other train stops every $6$ minutes. - Both stop together at midday (time $0$). 3. **Use the formula:** The trains will next stop together at the least common multiple (LCM) of their stopping intervals. 4. **Calculate the LCM:** - Prime factors of $9$ are $3^2$. - Prime factors of $6$ are $2 \times 3$. - LCM is the product of the highest powers of all primes: $2 \times 3^2 = 2 \times 9 = 18$. 5. **Interpretation:** The trains will next stop together $18$ minutes after midday. **Final answer:** $$18$$ minutes later.