To find the least common multiple (LCM) of 12 and 8, we can use the following method:
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Prime Factorization:
- The prime factorization of 12 is \(2^2 \times 3^1\).
- The prime factorization of 8 is \(2^3\).
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Identify the Highest Power of Each Prime:
- The prime factors involved are 2 and 3.
- For the prime number 2, the highest power between the factorizations is \(2^3\) (from 8).
- For the prime number 3, the highest power is \(3^1\) (from 12).
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Multiply the Highest Powers Together: \[ \text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24 \]
Thus, the least common multiple of 12 and 8 is \(\boxed{24}\).