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

Given:

The sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF.

To find:

The product of two numbers.

Solution:

Let LCM be x and HCF be y.

Then, by given condition,

Sum of LCM and HCF x + y = 1260 (1)

Also,

LCM is 900 more than HCF i.e.x = 900 + y

Substituting x = 900 + y in equation (1)

900 + y + y = 1260

900 + 2y = 1260

2y = 360 

y = 180

Then,

x = 900 + 180 = 108

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

Answer 2

LCM+ HCF= 1260

900+HCF +HCF=1260

900+ 2 HCF= 1260

2 HCF= 360

HCF= 180

LCM= 900+ 180= 1080

HCF* LCM= a*b= 180*1080= 194400

So, the correct option is B.