Question

The HCF of two natural numbers is 12. If the sum of the two numbers is 72, then the larger of the two numbers is
Options
12
48
24
none of these​

Answer 1

Given, HCF=12, LCM=72

One number =x, Other number =60−x

∴ Product of the two numbers = HCF × LCM

⇒x(60−x)=12×72

⇒x

2

−60x+864=0

⇒x

2

−36x−24x+864=0

⇒x(x−36)−24(x−36)=0

⇒(x−36)(x−24)=0

⇒x=36 or 24

∴ One of the number is 24.