To find the least common multiple (LCM) of 12 and 5, we can use the following steps:
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List the prime factors of each number:
- The prime factorization of 12 is \(2^2 \times 3^1\).
- The prime factorization of 5 is \(5^1\).
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Identify all the prime factors:
- The unique prime factors from both numbers are 2, 3, and 5.
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Take the highest power of each prime factor:
- For 2, the highest power is \(2^2\) (from 12).
- For 3, the highest power is \(3^1\) (from 12).
- For 5, the highest power is \(5^1\) (from 5).
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Multiply these together to get the LCM: \[ LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 \]
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Calculate the product: \[ 4 \times 3 = 12 \] \[ 12 \times 5 = 60 \]
Thus, the least common multiple of 12 and 5 is 60.