156592

For Alison’s and Sam’s statement, we need numbers that end in 0, and is not a multiple of 4, for example, numbers like 10, 30, 50, 70, 90.
For Alison’s and Matt’s statement, we need even numbers that either ends in 0 or 5, but it can’t be a multiple of 9, for example, numbers such as 15, 30, 60, 150.
For Sam’s and Matt’s statement, we need even numbers that are multiples of 3, but not multiples of 4 and 9, for example, numbers like 30, 60.
There are many triangular numbers, but not all of them can satisfy all four statements.
The lowest number to satisfy all four statements is 210.