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Prove that LCM of n numbers is n×min{n numbers} and HCF is max{n numbers}/n

Source: MTRP 2015 Class 11-Short Answer Type Question: Problem 5 :-

September 22, 2020

number theoryleast common multiplegreatest common divisor

Problem Statement

Let

a

be the smallest and

A

the largest of

n

distinct positive integers. Prove that the least common multiple of these numbers is greater than or equal to

n a

and that the greatest common divisor is less than or equal to

\frac{A}{n}