First I listed all the numbers up to 100(or as close as possible) for each of the 4 conditions.
After doing this I found numbers that appeared more than once on the entire list. I listed these down and found 7 pairs of numbers and 5 sets of three numbers. After finding all these I kept moving the numbers up until I found a common number through all conditions. This number (which is the lowest to meet all four statements) was 210.
Alison and Sam's statements had a pattern. Both started at 10 and for every 4 numbers for Alison was the same number as every 5th number in matt's pattern. Each time the number was increased by 20.
Alison and Matt's statements also have a reoccurring pattern. The first common number is 15. the next common number occurs when Alison's number is increased 3 times and Matt's number is increased by 3 also. After this, there is no clear pattern but there is possibly a pattern that increases by a lot every time.