Question

The Product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the Numbers ?​

Answer 1

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Answer :

Let the no be x and y.

Then, x - y =2

Now, the product of lcm and hcf of two no = product of two no

Accordingly, lcm× hcf = x×y.

=x×y = 24.

From eq 1- x =2+y

•Putting the value of x in eq 2,

(y+2)y= 24 = y2(square) + 2y - 24 =0

=y² + 6y - 4y -24= 0

= y(y+6) - 4(y+6) =0

= (y+6)(y-4)= 0

= y=-6 and y= 4.

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