152887

First of all I wrote down all the multiples of 2,3 and 4 then found my first sequence
1)2,3,4
Then I found my next sequence which was
2) 14,15,16
and realised that the first multiple of 2 in the sequence is 2 then the next one was 14 so I knew the difference between 2 and 14 was 12 but before I could say that was the rule I had to investigate more and checked with the other numbers. For both of the other numbers' I saw the difference was 12 too.
15-3=12 and 16-4=12 so I thought maybe I should try out the other numbers
3)26,27,28
The same pattern appeared again for the next ones 26-12,27-15 and 28-16 the answers were all 12. I carried on checking my answers
4)38,39,40
5)50,51,52
6)62,63,64
7)74,75,78
8)86,87,88
9)98,99,100
10)110,111,112