Count Connected Components in LCM Graph

Count the connected components of a graph where nodes are the given numbers and an edge exists between a and b iff lcm(a,b) ≤ threshold. The algorithmic challenge is to avoid O(n^2) pairwise checks for up to 1e5 numbers by exploiting the small threshold and divisor/multiple relationships (e.g., grouping via factors) to efficiently union connected nodes.