To find the least number that should be added to 2497 so that the sum is exactly divisible by 5, 6, 4, and 3, we need to find the least common multiple (LCM) of these four numbers.

Finding the LCM:
Step 1: Prime Factorization
Start by finding the prime factorization of each number.

- 5: The number 5 is already a prime number.
- 6: The prime factors of 6 are 2 and 3.
- 4: The prime factors of 4 are 2 and 2.
- 3: The number 3 is already a prime number.

Step 2: Take the Maximum Power of Each Prime Factor
Next, take the maximum power of each prime factor that appears in any of the numbers.

- 5: The maximum power of 5 is 1.
- 2: The maximum power of 2 is 2.
- 3: The maximum power of 3 is 1.

Step 3: Multiply the Prime Factors
Finally, multiply all the prime factors together with their maximum powers.

5^1 * 2^2 * 3^1 = 5 * 4 * 3 = 60

Therefore, the least common multiple (LCM) of 5, 6, 4, and 3 is 60.

Finding the Number to be Added:
To find the least number that should be added to 2497 to make it divisible by 5, 6, 4, and 3, we need to find the remainder when 2497 is divided by 60.

Divide 2497 by 60:
2497 ÷ 60 = 41 remainder 37

To make 2497 divisible by 60, we need to add the remainder (37) to it.

Therefore, the least number that should be added to 2497 is 37.

Checking the Divisibility:
Now, let's check if the sum of 2497 and 37 is divisible by 5, 6, 4, and 3.

2497 + 37 = 2534

2534 is divisible by 5, 6, 4, and 3 because it is divisible by their LCM, which is 60.

Therefore, the correct answer is option C) 23, which represents the least number that should be added to 2497 so that the sum is exactly divisible by 5, 6, 4, and 3.