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

Step 1: Find the LCM of 3, 4, 5, and 6.

• The prime factorization of 3 is $3$.
• The prime factorization of 4 is $2^2$.
• The prime factorization of 5 is $5$.
• The prime factorization of 6 is $2 \times 3$.

To find the LCM, we take the highest power of each prime factor:

• Highest power of 2: $2^2$
• Highest power of 3: $3$
• Highest power of 5: $5$

Thus, the LCM of 3, 4, 5, and 6 is:

$\text{LCM} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60$

Step 2: Find the remainder when 2497 is divided by 60.

We need to find out how much we need to add to 2497 to make it divisible by 60.

Divide 2497 by 60:

$2497 \div 60 = 41 \text{ remainder } 37$

So, when 2497 is divided by 60, the remainder is 37.

Step 3: Calculate the least number to add.

To make 2497 divisible by 60, we need to add enough to reach the next multiple of 60. Since the remainder is 37, we need to add:

$60 - 37 = 23$

Thus, the least number that should be added to 2497 is 23.

Final Answer:

The least number that should be added to 2497 so that the sum is divisible by 3, 4, 5, and 6 is 23.

Would you like more details or have any questions about the process?

Here are 5 related questions you might find interesting:

1. How do we find the LCM of more than two numbers?
2. Why is the remainder important when finding divisibility conditions?
3. How would the process change if we needed divisibility by different numbers?
4. Can you solve for the least number added to make a number divisible by 7, 11, and 13?
5. What is the general method for finding the least number to be added for divisibility conditions?

Tip: When dealing with divisibility problems, always start by finding the LCM of the divisors, as it helps in determining the exact condition for divisibility.