How many pairs of natural numbers exist such that when the LCM of the numbers is added to their sum a total of 49 is obtained?1236

To solve this problem, we need to understand the concept of LCM (Least Common Multiple) and how it relates to the sum of two natural numbers.

Step 1: Understand the problem The problem is asking for pairs of natural numbers (a, b) such that LCM(a, b) + a + b = 49.

Step 2: Identify possible pairs We know that the LCM of two numbers is always greater than or equal to the larger number. Therefore, the sum of the two numbers must be less than 49. We can start by identifying pairs of numbers that add up to less than 49.

Step 3: Check each pair For each pair of numbers (a, b), we calculate the LCM and check if LCM(a, b) + a + b = 49. If it does, we have found a valid pair.

Step 4: Count the pairs We count all the valid pairs we have found.

However, without a specific range for the natural numbers, it's impossible to provide a specific number of pairs. The problem needs to specify a range for the natural numbers to be considered.