The difference between two numbers is 12. The LCM of the two numbers is 133. Find the two numbers.

If the difference between two numbers is 12, those two numbers may be:

13 ... 1

14 ... 2

15 ... 3

16 ... 4

etc ...

We can ignore numbers which can be divided by themselves (like 2 ... 14 or 4 ... 16), so we have:

13 ... 1

17 ... 5

19 ... 7

20 ... 8

21 ... 9

22 ... 10

Let's stop here and find LCMs of given numbers:

13 ... 1 = 13

17 ... 5 = 85

19 ... 7 = 133

20 ... 8 = 40

21 ... 9 = 63

22 ... 10 = 110

So as we can see the numbers we're looking for are 19 and 7.