I showed LCA reduces to RMQ (via Euler tour). The reverse is also true: RMQ reduces to LCA.
Given an array, build a Cartesian tree where each node's value is the minimum of its subtree.
Then equals the value at . Why care?
Some LCA structures (like binary lifting) are simpler to implement than sparse tables. Also, this connection is theoretically interesting: RMQ and LCA are equivalent problems. Any preprocessing, query solution for one gives the same for the other.