  Let $M(n)$ denote the number of distinct entries in the $n \times n$
multiplication table. The function $M(n)$ has been studied by Erd\H{o}s,
Tenenbaum, Ford, and others, but the asymptotic behaviour of $M(n)$ as $n \to
\infty$ is not known precisely. Thus, there is some interest in algorithms for
computing $M(n)$ either exactly or approximately. We compare several algorithms
for computing $M(n)$ exactly, and give a new algorithm that has a subquadratic
running time. We also present two Monte Carlo algorithms for approximate
computation of $M(n)$. We give the results of exact computations for values of
$n$ up to $2^{30}$, and of Monte Carlo computations for $n$ up to
$2^{100,000,000}$, and compare our experimental results with Ford's
order-of-magnitude result.
