Another Farmer's Apple Challenge
A farmer has $N$ apples. He knows that when he makes groups of $2$, there is $1$ left over. When he makes groups of $3$, there are $2$ left over. When he makes groups of $4$, there are $3$ left over. This continues for groups of $5$ and $6$, leaving $4$ and $5$ apples left over, respectively. What is the least amount of apples he can have?