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

Correct option is (B) 194400

Let both numbers are a and b.

Also let LCM and HCF of both numbers a and b are L and H respectively.

According to given conditions,

L+H = 1260   __________(1)

L = 900+H     __________(2)

\(\therefore\) 900+2H = 1260   (From (1) & (2))

\(\Rightarrow\) 2H = 1260 - 900 = 360

\(\Rightarrow\) \(H=\frac{360}2=180\)

\(\therefore\) L = 900+180 = 1080

Now, product of both numbers = Product of their HCF and LCM.

i.e., a \(\times\) b = HCF (a, b) \(\times\) LCM (a, b)

\(\therefore\) Product of both numbers \(=H\times L=180\times1080\)

= 194400

Correct option is B) 194400