Question

If the sum of two numbers is 721 and LCM is 103 then what are numbers.

Answer 1

(1,6), (2,5)

Given:

LCM = 103

Sum of two numbers is 721

X = 103a & Y = 103b; where a & b are co-prime to each other.

Now, X+Y=721

=> 103a+103b=721

=> 103(a+b) = 721

=> a+b = 7

So, we have two conditions with us now. (a + b) is 7 and a and b are co-prime to each other.

Possible pairs of a & b are: (1,6), (2,5)

Answer 2

Sum of two numbers is $721$..   ( Given)

LCM of two numbers is  $103$  ..(given)

let consider the numbers are ,P  & Q

P = 103a

Q  = 103b              (  a & b are co-prime to each other)

According the question :-

P + Q =721

∴103a + 103b=721

103(a+b) = 721

( a + b) = $\frac{721}{103}$

( a+b) = 7

Hence (a + b) is 7

as ( a) and (b) both are co-prime to each other.

Now the pairs will be , either (1,6), or (2,5)

Ans :- The numbers pairs will be either (1,6), or (2,5).