  We study the Schwarzschild and Reissner-Nordstr\"{o}m black hole
thermodynamics using the simplest form of the generalized uncertainty principle
(GUP) proposed in the literature. The expressions for the mass-temperature
relation, heat capacity and entropy are obtained in both cases from which the
critical and remnant masses are computed. Our results are exact and reveal that
these masses are identical and larger than the so called singular mass for
which the thermodynamics quantities become ill-defined. The expression for the
entropy reveals the well known area theorem in terms of the horizon area in
both cases upto leading order corrections from GUP. The area theorem written in
terms of a new variable which can be interpreted as the reduced horizon area
arises only when the computation is carried out to the next higher order
correction from GUP.
