Question

the L.C.M of two number is 28 times of their H.C.F. The sum of their L.C.M and H.C.F is 1740.If one number is 240 then what is the other number.​

Answer 1

Let the H.C.F of two numbers be x

Then, LCM would be 28x

Given Sum of LCM and HCF = 1740

Therefore, x + 28x = 1740

29x = 1740

x = 1740÷29 = 60

So, HCF is 60 and LCM is 28×60 = 1680

Given one of the numbers = 240

let other be y

As we know,

LCM × HCF = Product of two numbers

Therefore, 1680×28 = 240y

47040 = 240y

47040 ÷ 240 = y

196 = y

Hence, the other number is 196