I. Find the Highest Common Factor (H.C.F.):
- 12a²b and 18ab²
- 15x³y²z and 25x²y&sup4;
- x² - 4 and x² + 4x + 4
- a(b - c) and b(b - c)
II. Find the Lowest Common Multiple (L.C.M.):
- 4a³ and 6a²b
- x² - y² and (x + y)²
- 10x²y, 15xy², and 20x³
III. Practical Application:
11. The Cookout Problem: You are hosting a neighborhood barbecue. Hotdogs are sold in packages of 10, but hotdog buns are sold in packages of 8.
- What is the minimum number of hotdogs you must serve so that every hotdog has a bun and there are no leftovers of either?
- Explain why this is relevant to the lesson. Is this an H.C.F. or an L.C.M. problem?