Question

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

Answer 1

let HCF be x
lcm= 900+x
sum= 1260
x+x+900=1260
2x=360
x=180 , LCM=180+900=1080

HCF*LCM= PRODUCT OF NUMBERS
180*1080= PRODUCT

194400= product

Answer 2

Given that the sum of HCF and LCM = 1260.

LCM + HCM = 1260  --------------------- (1)

Given that their LCM is 900 more than the HCF.

Let HCF = x.   ------------ (2)

Then the LCM = 900 + x.   ------------------- (3)


On solving (1),(2),(3).

1260 = x + (900 + x)

1260 = x + 900 + x

1260 = 2x + 900

1260 - 900 = 2x

360 = 2x

x = 360/2

x = 180.

Now, we got

HCF = 180.

Then, LCM = 900 + x

                   = 900 + 180

                   = 1080.



We know that product of two numbers = HCF * LCM

                                                                  = 180 * 1080

                                                                  = 194400.


Hope this helps!