Question

Sum of two numbera is 104 and their product is 2535 .what is the lcm

Answer 1

↑ Here is your answer ↓
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Let those numbers be 'x' and 'y',

Given that,

$x + y = 104 --(1)$

And,

$xy = 2535$

$y = 2535/x --(2)$

Sub (2) in (1),

$2535/x + x = 104$

Multiply throughout by 'x',

$x^2 + 2535 = 104x$

Open now,

$x^2 - 10x + 2535 = 0$

By solving the quadratic equation,

We get,

$x = 39$

Sub it again in any other equation,

$y = 2535/x$

$y = 2535/39$

$y = 69$

Now,

LCM of 69 and 39,

$69 = 3 * 23$

$39 = 3*13$

$=\ \textgreater \ 3*23*13$

$=\ \textgreater \ 897$

Cheers! :)

Answer 2

Answer: LCM=195

Step-by-step explanation:

• Given, the sum of two numbers is 104 and the product is 2535.
• Let the numbers be x and y.
• According to question,

                 x + y =104       (eq.1)

        and,  xy =2535        (eq.2)

        From eq.2  we get  y =$\frac{2535}{x}$.

• Putting the value of y in eq. 1 and solving;

         $x+\frac{2535}{x}=104$

     ⇒ $x^{2} -104x+2535=0$

• Solving the above equation we get x=39,65.

• Considering x=39 and putting in eq.2 we get y =65.

• Now, calculating the LCM of 39 and 65.

        39=3×13

        65=5×13

• LCM= 3×5×13

               = 195.

• Hence, the required LCM is 195 and the numbers are 39 and 65.

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