The integers $1, 2, 3, 4, 5$ and $6$ are written on a board. You can perform the following kind of move: select two of the numbers, say $a$ and $b$, such that $4a - 2b$ is nonnegative; erase $a$ and $b$, then write down $4a - 2b$ on the board (hence replacing two of the numbers by just one). Continue performing such moves until only one number remains on the board. What is the smallest possible positive value of this last remaining number?