I started by using trial and error to find three consecutive numbers where the first is a multiple of 2, the second a multiple of 3 and the third a multiple of 4.
I found 2, 3, 4 then 14, 15, 16 and then 26, 27, 28.
I noticed that to get from each set of consecutive multiples you add 12. I soon figured out that 12 was the lowest common multiple of the three numbers - 2,3 and 4
Then I tested this theory by adding 12 to the last set of consecutive multiples and found that this worked. Yay!
I then proceeded to trial the next set of numbers - 3,4 and 5. I found the lowest common multiple to be 60, so I added 60 to the three numbers and found that it makes a set of three consecutive multiples.
I tried this with the other given sets of numbers and found that they both worked as well!
I then wanted to challenge myself further! I used 2, 3, 4, 5, 6, 7, 8, 9 and 10! I tried to find nine consecutive numbers and I found out that the lowest common multiple is 2520. I added 2520 to the nine consecutive numbers and it made a set of consecutive multiples.
I found the lowest common multiple by multiplying 9, 8, 7, 6 and 10 because 9 covers 3, 8 covers 4 and 2 and 10 covers 5 and 6 is covered on it's own. I then divided it by 2 and 3 a couple of times to find the lowest one.