If the sum of LCM and HCF of 779 and 943 is divided by the sum of these two numbers, then what will be the remainder?

Correct option is D

Given:

The numbers are 779 and 943.

Formula Used:

HCF of two numbers a and b is given by HCF(a, b).

LCM of two numbers a and b is given by:

LCM(a, b) = $$\frac{(a × b) }{ HCF(a, b)}$$​​

Solution:

First, find the HCF of 779 and 943:

Using the Euclidean algorithm, we find that HCF(779, 943) = 41.

Now, calculate the LCM of 779 and 943:

LCM(779, 943) = $$\frac{(779 × 943) }{41}$$​ = 17,917

The sum of LCM and HCF is:

LCM + HCF = 17,917 + 41 = 17958

The sum of the two numbers is:

779 + 943 = 1,722

Now, divide the sum of LCM and HCF by the sum of the two numbers:

17958 ÷ 1,722 =   $$1722 \times 10 + 738 = 17958$$ 

Than the reminder = 738