public string GetMergeBase(string a, string b)
{
    using (var repo = new Repository("path/to/your/repo"))
    {
        var aCommit = repo.Lookup<Commit>(a);
        var bCommit = repo.Lookup<Commit>(b);
        if (aCommit == null || bCommit == null)
            return null;
        var baseCommit = repo.ObjectDatabase.FindMergeBase(aCommit, bCommit);
        return baseCommit != null ? baseCommit.Sha : null;
    }
}