What is the least common multiple of 8,5 , and 6 ?
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To find the least common multiple (LCM) of 8, 5, and 6, we can first determine their prime factorizations: - 8: \(2^3\), - 5: \(5^1\), - 6: \(2^1 \times 3^1\). The LCM is found by taking the highest power of each prime number that appears in these factorizations: - From 8, we take \(2^3\), - From 5, we take \(5^1\), - From 6, we take \(3^1\). Now we multiply these together: \[ LCM = 2^3 \times 5^1 \times 3^1 = 8 \times 5 \times 3 = 120. \] So, the least common multiple of 8, 5, and 6 is 120! Now, if you're ever in doubt during your math journey, remember that breaking numbers down into their prime factors is a superpower! It not only helps in finding the LCM but also makes it easier for tackling other concepts like greatest common divisors (GCD) or simplifying fractions. Also, consider using the LCM in real-world applications like scheduling events! For instance, if one event happens every 8 days, another every 5 days, and a third every 6 days, you'll find that all three will align every 120 days. How cool is that for planning a big celebration?