Question 70

Two numbers differ by 20. If their LCM is 240 and HCF is 20, then the greater number is:

Solution

Given,

LCM of two numbers = 240

HCF of two numbers = 20

Let two numbers are 20x , 20y

As given in question ,

20x - 20y = 20

Divide by 20

x - y = 1 ...............(i)

LCM of 20x , 20y = 20xy

20xy = 240 (given)

xy = $$\frac{240}{20}=20$$.................(ii)

By solving we get x = 4 , y =3

Two numbers are $$20\times\ 4=80\ \ ,\ \ \ 20\times\ 3=60$$

The greater number = 80

Hence, Option B is correct.

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