Final Answer:
The lowest common ancestor (LCA) of two given nodes in the provided binary search tree (BST) is 6.
Step-by-step explanation:
In a binary search tree (BST), the lowest common ancestor (LCA) of two nodes is the first node encountered while traversing from the root node, where the two given nodes lie in different subtrees or at least one of the nodes is the current node. In the given BST, to find the LCA of nodes 2 and 8, we start traversing from the root (6). Both nodes 2 and 8 lie on different sides of the root node, where 2 is in the left subtree, and 8 is in the right subtree of the root. Hence, the LCA for 2 and 8 must be the root node (6).
The BST's property aids in efficiently finding the LCA. Starting from the root node, comparisons are made to determine if the given nodes lie in the left or right subtree based on their values concerning the current node. This approach narrows down the search for the LCA, minimizing the traversal. In this instance, as both nodes 2 and 8 lie in different subtrees of the root, the LCA becomes the root node itself.
Additionally, the structure of a BST guarantees a sorted order, where values to the left of a node are smaller and values to the right are greater. This property further facilitates the LCA identification as it guides the search based on the values of the given nodes in relation to the current node during traversal, confirming that 6 is indeed the lowest common ancestor for nodes 2 and 8.