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

Let LCM be x and HCF be y.

Then, by given, x + y = 1260

Substituting x = 900 + y in above equation,

900 + y + y = 1260

900 + 2y = 1260

2y = 360

y = 180

Then, x = 900 + 180 = 1080

Thus, LCM = 1080 and HCF = 180

We know that for any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.

1080 × 180 = 194400