Question

The hcf of two numbers is 9.their lcm is 252.find their sum?

Answer 1

The sum of the HCF and LCM is 261

Answer 2

Ans: 99 or 261

Step by Step Explanation

Since HCF is 9, the numbers can be written as 9m and 9n where m and n are co-prime numbers.

We know that the product of two numbers is same as the product of their LCM and HCF

so 9mx9n=9/252

mn=28

so possible values of (m,n) are (1,28), (28,1), (2,14), (14,2), (4,7), (7,4)

Case 1:

(m,n) is (1,28) or (28,1)

Then the numbers are 9 and 252

So the sum is 261

Case 2:

(m,n) is (2,14) or (14,2)

These values cannot be taken as m and n are coprime numbers, here 2 and 14 are not coprime numbers

Case 3

(m,n) is (4,7) or (7,4)

Then the numbers are 36 and 63

So the sum is 99