10. (10 points) In a grade, Class One and Class Two participated in a tree planting activity. The total number of trees planted by both classes is the same, and it is between 205 and 300. In both classes, one person did not plant trees but provided water for everyone. In Class One, the rest of the students each planted 7 trees, and in Class Two, the rest of the students each planted 13 trees. Find the total number of students in both classes.
【Analysis】Since the total number of trees planted by the two classes is the same and is a multiple of 7 and 13, we need to find the least common multiple (LCM) of 7 and 13, then multiply it by an integer to get a number between 205 and 300. This number will be the total number of trees planted by each class. Dividing this number by 7 and adding 1 gives the number of students in Class 1, and dividing it by 13 and adding 1 gives the number of students in Class 2. Adding these together will give the total number of students.

【Solution】Solution: 7 and 13 are coprime,
so the least common multiple of 7 and 13 is $7 \times 13=91$,
$91 \times 3=273$ (trees),
$205<273<300$,
Number of students in Class 1: $273 \div 7+1=40$ (students),
Number of students in Class 2: $273 \div 13+1=22$ (students),
Total number of students: $40+22=62$ (students);
Answer: The total number of students in these two classes is 62 students.