To find the least common multiple (LCM) of 7 and 12, we can use the prime factorization method or the relationship between LCM and the greatest common divisor (GCD).
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Prime Factorization:
- The prime factors of 7 are \(7^1\).
- The prime factors of 12 are \(2^2 \times 3^1\).
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Identify the highest powers of all prime factors:
- The primes involved are 2, 3, and 7.
- The highest power of 2: \(2^2\)
- The highest power of 3: \(3^1\)
- The highest power of 7: \(7^1\)
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Multiply these together: \[ \text{LCM} = 2^2 \times 3^1 \times 7^1 = 4 \times 3 \times 7 \]
- First calculate \(4 \times 3 = 12\).
- Then calculate \(12 \times 7 = 84\).
Therefore, the least common multiple of 7 and 12 is \(84\).