Question

The product of two co-primes is 117. Their L.C.M should be
A.1
B.117
C.Equal to their HCF
D.Cannot be determined

Answer 1

Hint: If $a$ and $b$ are two numbers then the product of them is equal to the product of their LCM and HCF, that is , $a\times b=\text{HCF}\times \text{LCM}$. If two numbers are co-prime, they have only 1 as their common factor, then the HCF of two numbers is 1. Hence, calculate LCM by dividing the product of two numbers by their HCF.

Complete step-by-step answer:
The co-primes numbers are those numbers which do have any common factor.
The numbers are relatively prime.
If $a$ and $b$ are two numbers then the product of them is equal to the product of their LCM and HCF, that is , $a\times b=\text{HCF}\times \text{LCM}$
If two numbers are co-prime, they have only 1 as their common factor, then the HCF of two numbers is 1.
Also, we are given that the product of the two numbers is 117.
Therefore, LCM can be calculated by dividing the product of two numbers by their HCF.
Thus, LCM is ${\displaystyle \frac{117}{1}}=117$
If the product of two co-prime numbers is 117, then the LCM is 117.
Hence, option B is correct.

Note: The co-primes numbers are the numbers which do have any common factor with respect to each other. If two numbers are co-prime, then the HCF of those numbers is 1 and the LCM of those numbers is their product.