Also in this series: Tiling rectangles with F pentomino plus rectangles
The goal is to tile rectangles as small as possible with the V pentomino. Of course this is impossible, so we allow the addition of copies of a rectangle. For each rectangle $a\times b$, find the smallest area larger rectangle that copies of $a\times b$ plus at least one V-pentomino will tile. Examples shown, with the $1\times 1$, $1\times 2$ or $2\times 2$, you can tile a $3\times 3$ as follows:
Now we don't need to consider $1\times 1$, $1\times 2$, or $2\times 2$ any longer as we have found the smallest rectangle tilable with copies of V plus copies of each of those three.
There are at least 20 more solutions. I tagged it 'computer-puzzle' but you can certainly work some of these out by hand. The larger ones might be a bit challenging.