**Answer:** 2519 apples.

The amount of apples divided by 10 leaves a remainder of 9, the amount of apples divided by 9 leaves a remainder of 8, etc. So we're after a number of apples that divided by 10, 9, etc leaves a remainder of one less. This can be found by using the lowest/least common multiple of 10, 9, 8, 7, 6, 5, 4, 3 and 2, and then subtracting 1.