Find common root node for given nodes in a tree

gistfile1.cs

public class TreeAnalyzer
{
	public Node FindCommonRoot(IEnumerable<Node> nodes)
	{
		var walkedNodes = new HashSet<Node>();
		var branches = nodes.ToList();
		int nextIterationBranchRangeStartIndex = 0;
		do
		{
			for (int i = nextIterationBranchRangeStartIndex; i < branches.Count; i++)
			{
				nextIterationBranchRangeStartIndex = branches.Count;
				var node = branches[i];
				if (!walkedNodes.Contains(node))
				{
					walkedNodes.Add(node);
					branches.Add(node.Root);
					if(node.Root.Root == null)
					{
						// root node reached
						break;
					}
				}
			}	
		} while (OnlySingleBranchLeft(branches, nextIterationBranchRangeStartIndex));
		return branches[branches.Count - 1];
	}

	private bool OnlySingleBranchLeft(IList<Node> allBranches, int nextBranchesRangeStartIndex)
	{
		return allBranches.Count - nextBranchesRangeStartIndex == 1;
	}
}

public class Node
{
	public Node Root { get { throw new NotImplementedException();} }
	public IEnumerable<Node> Children { get { throw new NotImplementedException();} }
}