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

The correct option is (b) : 194400 .

Let HCF of two numbers be X and LCM of two numbers be y .  

Given : Sum of LCM and HCF of two numbers  

LCM is 900 more than HCF  

Put the value of y from eq 2 in  eq 1,

x + y = 1260

x + (x + 900) = 1260

2x + 900 = 1260

2x = 1260 - 900

2x = 360

x = 360/2

Put the value of x  in eq 2,

y = x + 900

y = 180 + 900

Product of two numbers =  Product of their LCM and HCF

Product of two numbers = 1080 × 180 = 194400

Hence, the Product of two numbers is 194400 .

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi there !
Here's the answer:

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Given,
HCF + LCM = 1260 ---(1)

& LCM = HCF + 900 ------(2)

Substitute (2) in (1)

=> HCF + (HCF + 900) = 1260
=> 2×HCF = 1260-900
=> 2×HCF = 360
=> HCF = 180

From(1) ,
LCM + 180 = 1260
=> LCM = 1260 - 180
=> LCM = 1080

We have,
Product of 2 No.s = (HCF of the two No.s ) × (LCM of the 2 No.s)

=> Product of two No.s = 180 × 1080

=> Product of two No.s = 194400


This Answer 194400 is in Option(b)

So Option b is correct


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