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It is well known that, when normalized by n, the expected length of a longestcommon subsequence of d sequences of length n over an alphabet of size sigmaconverges to a constant gamma_{sigma,d}. We disprove a speculation by Steeleregarding a possible relation between gamma_{2,d} and gamma_{2,2}. In order todo that we also obtain new lower bounds for gamma_{sigma,d}, when both sigmaand d are small integers.

On a Speculated Relation Between Chv\'atal-Sankoff Constants of Several Sequences