Question

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

Answer 1

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.