Question

The product of the LCM and HCF of two natural numbers is 24 . The difference of two numbers is 2 . Find the numbers..​

Answer 1

Let one number =x

Second number = x+2

Hence x*(x+2)=24

Or x^2+2x-24=0

I.e. (x+6)(x-4)=0

Now either x+6=0 i.e. x=-6

or x-4=0 i.e. x=4

Since the numbers are positive

Hence one numbers=x

And the second number=x+2=4+2= 6

4. and 4+2i.e. 6

4 and 6

Answer 2

Step-by-step explanation:

As we know,

LCM x HCF = a * b ( a & b are numbers)

=> ab = 24

& (a- b ) = 2 ………( given)

Since, ( a+ b)² = (a -b)² + 4ab… ( identity)

=> (a+ b)² = 2² + 4 *24

=> (a+ b)² = 4 + 96 = 100

=> a+ b = 10 or -10 ……… (1)

But a - b = 2 …………..(2)

By solving above 2 equations by taking a+ b= +10

We get, 2a = 12

=> a= 6

=> b = 4

But if we take a+ b = -10

We get a = - 6 , b = -4 But for LCM & HCF, negative values can be discarded..

So, the numbers are 6 & 4