What is the least common multiple of 4,12 , and \( 10 ? \)

To find the least common multiple (LCM) of 4, 12, and 10, we begin by determining the prime factors of each number: - 4 = \( 2^2 \) - 12 = \( 2^2 \times 3 \) - 10 = \( 2 \times 5 \) Next, we take the highest power of each prime number that appears in the factorization: - For 2, the highest power is \( 2^2 \) (from 4 or 12). - For 3, the highest power is \( 3^1 \) (from 12). - For 5, the highest power is \( 5^1 \) (from 10). Now, we multiply these together to get the LCM: LCM = \( 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60 \). So, the least common multiple of 4, 12, and 10 is 60! Did you know that the concept of the least common multiple has been around since ancient times? The ancient Greeks studied multiples and factors, making significant contributions to number theory. They would often use diagrams and geometrical approaches to understand the relationships between numbers, paving the way for modern mathematics! For a fun real-world application, think about planning events! If you want to sync the schedules of three different activities—say, a yoga class every 4 days, a team meeting every 12 days, and a tennis match every 10 days—knowing the LCM helps you figure out when all three will coincide. In this case, you’d see that all three activities happen on the same day every 60 days—a perfect way to plan a community day!