Relation between $|H \lor K|$ , $|H|$ and $|K|$

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Let $H$ and $K$ be subgroups of a finite group , then we know that the subgroup generated by $H \cup K$ i.e. $H \lor K$ is the smallest subgroup containing both $H$ and $K$ , then how can we relate the order of $H \lor K$ , $|H|$ and $|K|$ ?