Solution: Find the least common multiple (LCM) of 8 and 12. Prime factors of 8: $ 2^3 $, of 12: $ 2^2 \times 3 $. LCM is $ 2^3 \times 3 = 24 $. \boxed{24}

["How to Find the Least Common Multiple (LCM) of 8 and 12: A Simple Step-by-Step Guide", "Understanding the Least Common Multiple (LCM) is a fundamental skill in math that helps solve problems involving fractions, scheduling, and repeating cycles. One of the most common questions students and learners encounter is: What is the LCM of 8 and 12? This article breaks down the solution using prime factorization, making it easy to find the LCM and confirm it equals 24.", "---", "### Understanding LCM", "The Least Common Multiple of two or more numbers is the smallest positive number that both numbers can divide evenly. For example, the LCM of 8 and 12 is the smallest number even and divisible by both.", "---", "### Prime Factorization of 8 and 12", "To find the LCM, start by breaking each number into its prime factors:", "- Prime factors of 8:\n $ 8 = 2 \ imes 2 \ imes 2 = 2^3 $", "- Prime factors of 12:\n $ 12 = 2 \ imes 2 \ imes 3 = 2^2 \ imes 3 $", "---", "### Using Prime Factorization to Calculate LCM", "To determine the LCM, take the highest power of each prime number appearing in the factorizations:", "| Prime | In 8: $ 2^3 $ | In 12: $ 2^2 \ imes 3 $ | Highest Power |\n|-------|----------------|--------------------------|---------------|\n| $ 2 $ | $ 2^3 $ | $ 2^2 $ | $ 2^3 $ |\n| $ 3 $ | — | $ 3^1 $ | $ 3^1 $ |", "Multiply these together to get the LCM:\n$$\n\ ext{LCM} = 2^3 \ imes 3 = 8 \ imes 3 = 24\n$$", "---", "### Why This Method Works", "Using prime factorization ensures you always find the least common multiple — no guessing, no listing multiples, just sharp logic. This method works for any pair of numbers and forms a reliable foundation for solving more complex LCM problems.", "---", "### Real-Life Applications of LCM", "- Scheduling: If one event occurs every 8 days and another every 12 days, they will coincide every 24 days — thanks to LCM.\n- Fractions: Finding a common denominator in fractions like $ \frac{1}{8} $ and $ \frac{1}{12} $ requires the LCM of 8 and 12, which is 24.", "---", "### Final Answer:\nThe least common multiple of 8 and 12 is\n$$\n\boxed{24}\n$$", "Mastering LCM through prime factorization empowers you to tackle math problems with confidence. Practice with different numbers, and watch how this simple yet powerful concept simplifies real-world challenges!"]