a)

Pencils :
60 = 60 x 1
= 30 x 2
= 20 x 3
= 15 x 4
= 12 x 5
= 10 x 6


Erasers :
45 = 45 x 1
= 15 x 3
= 9 x 5

Notice that the largest common factor between the two numbers is 15.

60 = 15 x 4
45 = 15 x 3

So the largest possible number of students in the class is 15, where each student receives 4 pencils and 3 erasers.

b) When you have more students, each student will get less pencils/erasers since you have to divide the same number of pencils and erasers among more students.

When the largest possible number of students in the class is reached, the number of erasers and pencils each student receives is the smallest possible.

So, the least number of pencils each student would have received = 4