## 33. Least Number

What is the least number that, when divided by $2, 3, 4, 5$, and 6, gives remainders of $1, 2, 3, 4$, and 5 respectively?
33. Let $n$ be an unknown number. Since $n$ when divided by 2 leaves a remainder of 1, the number $n+1$ is divisible by 2. Since $n$ when divided by 3 leaves a remainder of 2, the number $n+1$ is divisible by 3, and so on. Similarly, $n+1$ is divisible by 4, 5, and 6. But the least common multiple of 2, 3, 4, 5, and 6 is 60. Therefore, $n=59$.