  This paper shows that a simple algorithm produces the {\em
all-prefixes-LCSs-graph} in $O(mn)$ time for two input sequences of size $m$
and $n$. Given any prefix $p$ of the first input sequence and any prefix $q$ of
the second input sequence, all longest common subsequences (LCSs) of $p$ and
$q$ can be generated in time proportional to the output size, once the
all-prefixes-LCSs-graph has been constructed. The problem can be solved in the
context of generating all the distinct character strings that represent an LCS
or in the context of generating all ways of embedding an LCS in the two input
strings.
