Question

The product of LCM and HCF of two numbers is 48. The difference of two numbers is 8. Find the numbers?
18​

Answer 1

Answer: 12,4 or -4, -12

Step-by-step explanation: Let one of the numbers be x and the other number be x-8 since the difference between them is 8.

LCM * HCF = x * (x-8)

=> 48 = x^2 - 8x

=> x^2 - 8x - 48= 0

=> x^2 - 12x + 4x - 48=0

=> x(x-12) +4 (x-12) =0

=> (x-12) (x+4)=0

=> x=12 or x= -4

Now,

putting x=12 we get,

one number= 12, and

other number= 12-8 = 4

Or,

putting x= -4 we get,

one number = -4, and

other number= - 4 - 8= -12

Therefore, the number can be 12, 4 or -4, -12.

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