Copied from the Knot Atlas and annotated. As you see, $7_2$ needs $4$ braid strands (any rational knot needs at most 4), but if we cheat and define "closure" differently, we could say "The knot $7_2$ can be mapped to a $2$-tangle, which can be obtained by a Temperley-Lieb closure (of the lowest $2$ strands) of a braid which only needs $3$ strands".
My question: I think any rational knot (or link) needs only $3$ strands. (This even is a cool possibility to assign a binary number to it.) Is this correct?