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.