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Orders in Products: Group $G \times H$

ABSALG-4XJU5W

Suppose the element $a$ has order $m$ in the group $G$, and the element $b$ has order $n$ in the group $H$.

What is the order of the pair $(a,b)$ in the group $G\times H$?

A

$mn$

B

LCM$(m,n)$

C

GCD$(m,n)$

D

$m+n$

E

Max$(m,n)$

F

Min$(m,n)$