Analysis: In order to exchange the hundred digits with the ten digits, the actual number of people is less 180, and the hundred digits must be 2 larger than the ten digits. Then according to the meaning of the question, it should be above 970. Considering that it is a multiple of 36, then:

970 ÷ 36 = 26 Yu 34

The remainder 34 is 2 less than 36.

So this school can have 970+2=972 students at most.