Question

The HCF of two numbers is 36 and their sum is 1260. If both are 3 digit numbers, then how many such pairs of numbers are possible?​

Answer 1

Step-by-step explanation:

Let the HCF be x

LCM=HCF+900

LCM=x+900 --(1)

And

LCM+HCF=1260

LCM+x=1260 --(2)

From (1) and (2)

(x+900)+x=1260

2x+900=1260

2x=1260−900

2x=360

x= 360/2

x=180

HCF =180

And, from (1),

LCM=HCF+900

LCM=180+900

LCM=1080

By formula, product of the numbers is equal to the product of their HCF and LCM.

Product of numbers =HCF×LCM

=180×1080

Product =194400