the point of the LMM is to evolve several different rates simultaneously. If you rates $f_i$ from $t_i$ to $t_{i+1}$ and take a bond expiring at $t_j$ as numeraire then only the rate $f_{j-1}$ is driftless.

Typically $P_{t_0}$ is used as numeraire which makes all the rates have drift. It generally gives lower variance.

(see my book More mathematical finance for extensive discussion of drifts.)

the point of the LMM is to evolve several different rates simultaneously. If you have rates $f_i$ from $t_i$ to $t_{i+1}$ and take a bond expiring at $t_j$ as numeraire then only the rate $f_{j-1}$ is driftless.

Typically $P_{t_0}$ is used as numeraire which makes all the rates have drift. It generally gives lower variance.

(see my book More mathematical finance for extensive discussion of drifts.)