Final Shape After Repeated Square Cuts from Rectangle

Daniel takes a sheet of paper of dimensions $m \times n$, where $m$ and $n$ are positive integers, and cuts off a square from the shorter side. He then discards this square and continues the process by cutting off another square from the remaining rectangle, repeating this until no further squares can be cut. The cuts must follow the grid lines of the paper. What will Daniel be holding in his hands when he completes this process and begins to tidy up?