Questions about the number of apples

In the orchard, growers prepare to harvest the apples every 10 bags well, but at the end of the pack, there are 9 left. If the number of 9 points, the remaining 8, so the grower will press 8 points, the result is more than 7, according to 7 points, more than 6, according to 6 points, more than 5. So, the growers forget about them. Divide the total number of apples by 5, remainder 4, divided by 4, 3, divided by 3, 2, divided by 2, and 1.

Do you know how many of these apples there are at least?

Analysis: No matter how points, always missing an apple. So, if there is one more apple, then this number can be 10, 9, 8, 7, 6, 5, 4, 3, 2 to be exhausted. (Because dividing by 10 more than 9 is equivalent to dividing by more than 5 4, dividing by 9 + 8 is equivalent to dividing by 3 + 2, ...). The problem is then translated into the least common multiple of 10, 9, 8, 7, 6. As you can see from the answer to this question, this number should be a multiple of 2520 or 2520. So the number of apples must be at least 2,519.

Questions about the number of apples