Note that, in order to have a GCF of 6, each number has to be divisible by 6. If we want to just test a bunch of numbers, we don't have to test 1, 2, 3, 4, 5. We just have to test 6, 12, 18, 24, 30, . . .
Number 1, number 2, LCM, GCF
6, 12, 12, 6
12, 18, 36, 6
18, 24, 72, 6
24, 30, 120, 6
The two numbers are 24 and 30.