6. (10 points) For a certain project, if working alone, Team A needs 24 days, Team B needs 36 days, and Team C needs 60 days; it is known that all three teams worked for an integer number of days, and the task was completed within 18 days (including 18 days). How many days did Team A work at least? $\qquad$ days.
【Solution】Solution: According to the problem, we know:
The efficiency of A, B, and C is: $\frac{1}{24}, \frac{1}{36}, \frac{1}{60}$. To minimize the number of days A works, B and C need to work more days. When B works exactly 18 days, the total work done is $18 \times \frac{1}{36}=\frac{1}{2}$.
When B works for 18 days, the remaining work cannot be completed by C in an integer number of days.
Then, analyzing the divisors of 60, if C works for 15 days, the work done by C is: $\frac{1}{60} \times 15=\frac{1}{4}$. The number of days A works is: $\left(1-\frac{1}{2}-\frac{1}{4}\right) \div \frac{1}{24}=6$ (days)
Therefore, the answer is: 6