Because when we add 51and 34 we get 85
after that when we will find LCM of 51 and 34 we will
find 102. okkkk

Explanation:

To solve this problem, we need to find two natural numbers that satisfy two conditions: their sum is 85, and their least common multiple (LCM) is 102.

Condition 1: The sum of the two numbers is 85.
Let's assume the two numbers are x and y. According to the given condition, we have the equation:
x + y = 85

Condition 2: The least common multiple (LCM) of the two numbers is 102.
The LCM of two numbers is the smallest multiple that both numbers divide evenly into. In this case, we have the equation:
LCM(x, y) = 102

To find the answer, we can solve these two equations simultaneously.

Solving the equations:
We can solve the first equation for x:
x = 85 - y

Substituting this value of x into the second equation, we have:
LCM(85 - y, y) = 102

Prime Factorization:
To find the LCM, we need to factorize the numbers. The prime factors of 102 are 2, 3, and 17.

The prime factors of 85 - y can be found by subtracting the prime factors of y from the prime factors of 85. The prime factors of 85 are 5 and 17.

Setting up the equation:
Using the prime factorization, we can set up the equation:
2 * 3 * 17 = (2 * 5 * 17) * y'

Simplifying the equation:
2 * 3 = 5 * y'

6 = 5 * y'

Finding the value of y:
Dividing both sides of the equation by 5, we find:
y' = 6/5

Since y is a natural number, y' must be a whole number. Thus, y' can be 1 or 6.

If y' = 1, then y = 5. Substituting this value of y into the first equation, we find:
x = 85 - 5 = 80

If y' = 6, then y = 30. Substituting this value of y into the first equation, we find:
x = 85 - 30 = 55

Conclusion:
The two natural numbers that satisfy both conditions are 80 and 5, or 55 and 30. Among the given options, the correct answer is option 'D' (51 and 34).