Question

If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, then the product of two numbers is
A. 203400
B. 194400
C. 198400
D. 205400

Answer 1

Answer:

Product of two numbers is 194400 .

Step-by-step explanation:

Let the LCM of two numbers be L

and HCF of two numbers be H

• First condition states that sum of LCM and HCF of two numbers is 1260, i.e.;

                    L + H = 1260

                      L = 1260 - H ---------- [Equation 1]

• Second condition states that LCM is 900 more than their HCF, i.e.;

                     L = 900 + H

                  1260 - H = 900 + H  {using equation 1}

                    2*H = 1260 - 900

                      H = 360/2 = 180

Putting value of H in equation 1, we get; L = 1260 - 180 = 1080

So, HCF of two numbers = 180  and  LCM of two numbers = 1080

Now, Product of two numbers = HCF * LCM

                                                  = 180 * 1080 = 194400 .

Answer 2

HEY FRIEND HERE IS UR ANSWER ,

Given that the sum of HCF and LCM = 1260.

LCM + HCM = 1260  --------------------- (1)

Given that their LCM is 900 more than the HCF.

Let HCF = x.   ------------ (2)

Then the LCM = 900 + x.   ------------------- (3)

On solving (1),(2),(3).

1260 = x + (900 + x)

1260 = x + 900 + x

1260 = 2x + 900

1260 - 900 = 2x

360 = 2x

x = 360/2

x = 180.

Now, we got

HCF = 180.

Then, LCM = 900

                   = 900 + 180

                  = 1080.

                  

We know that product of two numbers = HCF * LCM

                                                                 = 180 * 1080

                                                                 = 194400.

HOPE IT HELPS :)

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