We show that two different problems, the statistics of scaled height in a (1+1)--dimensional anisotropic Ballistic Deposition (BD), and the statistics of the Longest Common Subsequence (LCS) of a pair of random sequences drawn from c letters for c>>1, share the same Tracy-Widom distribution of the largest eigenvalue of random GUE-matrices. Our result is derived via the mapping of BD and LCS to the exactly solvable (2+1)--anisotropic directed percolation (ADP) and subsequent application of exact results known for the Ulam problem. (Refs: S.N.Majumdar, S.Nechaev, PRE 69, 011103 (2004); S.N.Majumdar, S.Nechaev, q-bio.GN/0410012)