To solve this problem, Tommy needs to determine the least common multiple (LCM) of the number of hot dogs in a pack (10) and the number of buns in a pack (8). The LCM will represent the least number of hot dogs and buns such that there’s no leftover.

Steps to Solve:

1. List multiples of each number:

   • Multiples of 10: $10, 20, 30, 40, 50, \ldots$
   • Multiples of 8: $8, 16, 24, 32, 40, 48, \ldots$

2. Find the least common multiple:

   • The smallest number that appears in both lists is 40.

3. Determine how many packs are needed:

   • To get 40 hot dogs, Tommy needs $40 \div 10 = 4$ packs of hot dogs.
   • To get 40 buns, Tommy needs $40 \div 8 = 5$ packs of buns.

Final Answer:

• Hot dogs: 4 packs
• Buns: 5 packs

Would you like me to explain further or clarify any steps?

Here are some related questions for further understanding:

1. How do we find the LCM of larger numbers?
2. What are prime factors, and how are they used to find the LCM?
3. Why is it important for the numbers of hot dogs and buns to match?
4. What if the pack sizes were different, e.g., 6 and 9?
5. How can you apply the concept of LCM in other real-life situations?

Tip: When calculating the LCM, listing the prime factorization of each number often makes the process easier for larger numbers.