A man had to pack a sack of apples into packets but as each packet had to have exactly the same number of apples he was having difficulty. If he packed 10 apples per packet, one packet only had 9. If he packed 9 apples per packet, one packet only had 8. If he packed 8 apples per packet, one packet only had 7. If he packed 7 apples per packet, one packet only had 6. And so on down to 2 apples. How many apples did he start with?

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Solution:

2519 apples.

The solution for the answer is the LCM (Lowest Common Multiple) of 10,9,8,7,6,5,4,3,2,1 minus 1. LCM would give the least number which is divisible by all of these number and subtracting one would give us the number of apples which were initially there.