Question

If two numbers $a$ and $b$ are such that they are relatively prime, find their LCM.

Answer 1

Hint: If two numbers are relatively prime, they don’t have any common factors except 1. And we know that the LCM of two numbers is the lowest possible number which is a multiple of both $a$ and $b$. In this case, the LCM will be the product of two numbers.

Complete Step-by-Step solution:
Given that the two numbers $a$ and $b$ are relatively prime numbers. So they don’t have any common factors except 1.
We have to determine their LCM and we know that the LCM of two numbers is the lowest possible number which is a multiple of both $a$ and $b$.
But in this case, their lowest common multiple will be the product of the numbers itself because we are not getting any common factor from them to be taken out. Therefore we have:
$ \Rightarrow $ LCM of $a$ and $b$ $ = a \times b$.

Note: If two numbers are relatively prime, their LCM is the product of the two numbers and their HCF is 1. These basic standard results can be used to solve more complex problems of such type. LCM is known as Least Common Multiple.