  In this paper, we propose a pseudo polynomial size LP formulation for finding
a payoff vector in the least core of a weighted voting game. Both the number of
variables and number of constraints in our formulation are bounded by
$\mbox{O}(Wn)$ where $W$ is the total sum of (integer) voting weights and $n$
is the number of players. When we employ our formulation, a commercial LP
solver calculates a payoff vector in the least core of practical weighted
voting games in a few seconds. We also extend our approach to vector weighted
voting games.
