Relation between the Highest Common Factor (HCF), Least Common Multiple (LCM) and Common Ratio of Geometric Progression (G.P) [For Finite Number of Terms]

There are two different theorems both are for finite number of terms (n). First theorem is for even number of terms (n) and second is for odd number of terms. Highest Common factor (HCF) of a geometric progression (GP) is always its first term and least Common Multiple (LCM) of a Geometric progression is always it's last term.