Question

The hcf of two numbers is 12 and their lcm is 72. Find the product of the two numbers.

Answer 1

Answer:

Let the two numbers be x and y.

We know that.. product of two numbers = HCFx LCM.

Therefore XY= 12 x 72= 864….(1)

According to given condition, their sum is 60

Therefore x+y = 60……….(2)

We know that

(x-y)² =(x+y)² -4xy

Substitute values from 1 & 2

(X-y)² = 3600–4x864=144

X-Y =√144= 12…(3)

By solving 2 and 3

We get x=36 and y=24.

Step-by-step explanation:

one more answer is there

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.