In a school, the number of students in Grades 6, 7, and 8 was 180, 270, and 405, respectively. Students in each grade were divided into different sections, but every section across grades had the same number of students. For each section, a class teacher was appointed. What was the minimum number of clan teachers required for the purpose?

Since the students in each grade were divided into different sections, and every section across grades had the same number of students, the minimum number of sections across grades will be the HCF of the numbers of students in Grades 6,7, and 8. HCF (180, 270, and 405= 45 Number of students in each class = 45 Number of sections in grade 6 = 180/45 = 4 Number of sections in grade 7 = 270/45 = 6 Number of sections in grade 8 = 405/45 = 9 Minimum number of sections = 4+6+9=19.