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Groups and FieldsMediumSubgroups and Cyclic Groups

Subgroups and Cyclic Groups · Medium problem

Elements g,hg,h of a group commute, with ord⁡(g)=4\operatorname{ord}(g)=4, ord⁡(h)=9\operatorname{ord}(h)=9, and ⟨g⟩∩⟨h⟩={e}\langle g\rangle\cap\langle h\rangle=\{e\}. What is ord⁡(gh)\operatorname{ord}(gh)?