To find the least common multiple (LCM) of 7 and 12, we can use the prime factorization method.
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Prime factorization:
- The prime factorization of 7 is simply \( 7^1 \).
- The prime factorization of 12 is \( 2^2 \times 3^1 \).
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Take the highest power of each prime factor:
- For the prime factor 2: the highest power is \( 2^2 \).
- For the prime factor 3: the highest power is \( 3^1 \).
- For the prime factor 7: the highest power is \( 7^1 \).
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Multiply these together: \[ LCM = 2^2 \times 3^1 \times 7^1 = 4 \times 3 \times 7 \] \[ = 12 \times 7 = 84 \]
Therefore, the least common multiple of 7 and 12 is 84.
The correct response is: 84