The average (arithmetic mean) of 4 different integers is 75. if the largest integer is 90, what is the least possible value of the smallest integer?

For the least value of the smallest integer, select other integers the as large as possible. As all the digits are different, we select other two integers as 89 and 88. In order for the average to be 75 the sum should be 300.

so x+88+89+90=300

x+267 = 300

x = 300-267

x=33 so The least possible value of the smallest integer is 33.