Break the numbers down into their factors:
36=3*3*2*2
75=3*5*5
3 can't be broken down any further
The LCM needs to contain these factors without repeating unnecessarily. We need to have two threes because of 36; we also need two twos and two fives. The LCM is 2*2*3*3*5*5=900. If you look at how the LCM breaks down, you can see in there the 4 factors of 36 and the 3 of 75. The 3 is already one of these factors.