If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF,

Solution:

Let the HCF be x and the LCM of the two numbers be y.

It is given that the sum of the HCF and LCM is 1260

$x+y=1260 \ldots \ldots(i)$

And, LCM is 900 more than HCF.

$y=x+900 \ldots \ldots(i i)$

Substituting (ii) in (i), we get:

$x+x+900=1260$

$2 x+900=1260$

$2 x=1260-900$

$2 x=360$

$x=180$

Substituting $x=180$ in (ii), we get:

$y=180+900$

$y=1080$

We also know that the product the two numbers is equal to the product of their LCM and HCF

 

Thus the product of the numbers

$=1080(180)$

$=194400$

Hence, the correct choice is (b).