If mrs murphy separates her class into groups of 4 students each, 1 student is left over. if she separates her class into groups of 5 students each,2 students are left over. what is the least number of students the class could have ?

The question means that when the number is 1 more than a multiple of 4 and two more than a multiple of 5. Write out multiples of 4 with one added on to them.
5,9,13,17,21,
Then write out multiples of 5 with one added on to them
7,12,17,22,
The smallest number that both lists share is 17, so that is the answer