Question

Sum of the LCM and HCF of two numbers is 2790 and their difference is
2610. If one number is 270 then find the other.

Answer 1

LCM - HCF = 13900 which is indeed equal to 2610 + 10.

The other number is 103.

Let the other number be x.

We know that HCF (highest common factor) of 270 and x is 10 because 270 is divisible by 10 and x is a factor of 10.

We also know that LCM (lowest common multiple) of 270 and x is (270x/10) = 27x.

From the given information:

LCM + HCF = 2790

=> 27x + 10 = 2790

=> 27x = 2780

=> x = 103. Therefore, the other number is 103.

Now, we need to verify if the difference between the LCM and HCF of these two numbers is indeed 2610.

LCM(270, 103) = 13910

HCF(270, 103) = 10

Therefore, LCM - HCF = 13900 which is indeed equal to 2610 + 10.

Hence, the other number is 103.

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