Hello -
After listing the middle multiple (for example if you have to find three consecutive numbers where the first is a multiple of 2, the second is a multiple of 3 and the third is a multiple of 4, the middle multiple would be 3)
so...
2, 3, 4
5, 6, 7
3, 9, 10
11, 12, 13
You would need to write down the whole three times table then for each number you would write the number below and above, seeing if they are multiples of 2 and 4.
We found the following consecutive numbers using this method.....
14, 15, 16
26, 27, 28
38, 39, 40
50, 51, 52
62, 63, 64
74, 75, 76
86, 87, 88
Then we found a pattern...... (wait for it)
BOOM!
We saw that there was actually a much more simple and quick way to do this. You add the Lowest Common Multiple!!!!!!!!!!!!!!!!!!!!! Yaaaaaaaay!!!!!!!!!!
For this puzzle it is 12 ;)
We worked this out by finding the difference between the sequences. For example 26-14= 12
27-15= 12
40-28= 12
50-38= 12
51-39= 12
52-40= 12
etc.
You can use a lowest common multiple calculator to do this ;D