  Motivated by the observation of two distinct superconducting phases in the
moir\'eless ABC-stacked rhombohedral trilayer graphene, we investigate the
electron-acoustic-phonon coupling as a possible pairing mechanism. We predict
the existence of superconductivity with the highest $T_c\sim 3$K near the Van
Hove singularity. Away from the Van Hove singularity, $T_c$ remains finite in a
wide range of doping. In our model, the $s$-wave spin-singlet and $f$-wave
spin-triplet pairings yield the same $T_c$, while other pairing states have
negligible $T_c$. Our theory provides a simple explanation for the two distinct
superconducting phases in the experiment and suggests that superconductivity
and other interaction-driven phases (e.g., ferromagnetism) can have different
origins.
