10th Class Mathematics Real Numbers Question Bank MCQs - Real Number

The LCM and the HCF of two numbers are 1001 and 7 respectively. How many such pairs are possible?

A) 0

B) 1

C) 2

D) 7

Correct Answer: C

Solution :

Given, LCM =1001 and HCF =7

Let the two numbers be x and y.

\[\therefore \,\,x=7c\]and y = 7b, where c and b are coprimes.

We have, \[x\times y=LCM\times HCF\]

\[\Rightarrow \,\,7a\times 7b=1001\times 7\]

\[\Rightarrow \,\,\,ab=143\]

\[\Rightarrow \,\,\,\left( a,\,\,b \right)=\left( 1,143 \right)\] or \[\left( 11,\,13 \right)\]

There are two pairs of numbers.