Q:

Find the smallest positive integer that gives remainder 1 when divided by 2,3,4,5,6,7,8

The question states:

Find The smallest positive integer that gives the remainder 1 when it is divided by each of the numbers 2, 3, 4, 5, 6, 7, 8.

Any ideas on how to begin?

A:

Call the number you're looking for $x$. Then by definition, $x-1$ is a multiple of $2,3,...,8$. To find the smallest such $x-1$, find the least common multiple of these numbers. 

A:

Let $x $ be the number.
The $x -1 $ is a common multiple of 2,3,4,5,6,7,8.  To be the smallest number you somehow have to find the smallest common multiple.  The least common one, if you will.

