Question

The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.

Answer 1

Given:

The LCM of two numbers is 14 times their HCF.

The sum of LCM and HCF is 600.

One number is 280.

To find:

The other number.

Solution:

Let HCF of two numbers be x.

The LCM of two numbers is 14 times their HCF.

LCM = 14x

The sum of LCM and HCF is 600.

`14x+x=600`

`15x=600`

`x=(600)/(15)`

`x=40`

So, HCF = 40 and the LCM is

`LCM=14(40)`

`LCM=560`

We know that, if a and b are two numbers, then

`a* b=LCM(a,b)* HCF(a,b)`

One number is 280.

`280* b=560* 40`

`b=(560* 40)/(280)`

`b=2* 40`

`b=80`

Therefore, the other number is 80.