LCM of \( 20,22,24 \)

To find the least common multiple (LCM) of 20, 22, and 24, we first factor each number into its prime components: - \( 20 = 2^2 \times 5 \) - \( 22 = 2^1 \times 11 \) - \( 24 = 2^3 \times 3 \) Next, we take the highest power of each prime number present in the factorizations. We have: - Highest power of \( 2 \) is \( 2^3 \) (from 24) - Highest power of \( 3 \) is \( 3^1 \) (from 24) - Highest power of \( 5 \) is \( 5^1 \) (from 20) - Highest power of \( 11 \) is \( 11^1 \) (from 22) So, we multiply these together: \[ \text{LCM} = 2^3 \times 3^1 \times 5^1 \times 11^1 = 8 \times 3 \times 5 \times 11 \] Calculating it step-by-step: 1. \( 8 \times 3 = 24 \) 2. \( 24 \times 5 = 120 \) 3. \( 120 \times 11 = 1320 \) Therefore, the LCM of 20, 22, and 24 is \( 1320 \). Now, have you ever wondered where this concept comes from? The LCM isn't just for school math; it plays a role in various fields, like music and engineering. Think about musicians needing to play in sync; knowing the LCM of their rhythms helps ensure everyone is on the same beat! Also, a common mistake is to multiply all numbers outright and then try to find the LCM. This may give you a large number, but it won't necessarily be the lowest common multiple without considering the prime factorizations—so keep those factors in check!