What is the smallest number of children the class could have?

If a kindergarten teacher places her children 4 on each bench, there will be 3 children who will not have a place. However if 5 children are placed on each bench, there will be 2 empty places. What is the smallest number of children the class could have?

Let N be the number of children in the class.

If 4 children are placed on each bench, there will be 3 children left out.
=> N-3 is divisible by 4

If 5 children are placed on each bench, there will be 2 empty seats left out.
i.e. 3 children in one bench.
=> N-3 divisible by 5.

Hence N-3 should be divisible by 4 and 5 and smallest number divisible by 4 and 5 is 20.
=> N-3 = 20
=>N = 23

Smallest number of children the class could have is 23.