To find the least common multiple (LCM) of 7 and 12, we can use the prime factorization method.
- The prime factorization of 7 is: \(7\)
- The prime factorization of 12 is: \(2^2 \times 3\)
To find the LCM, we take the highest power of each prime factor:
- From 7, we take \(7^1\).
- From 12, we take \(2^2\) and \(3^1\).
Now, we can multiply these together to find the LCM:
\[ \text{LCM} = 2^2 \times 3^1 \times 7^1 = 4 \times 3 \times 7 \]
Calculating this step by step:
- \(4 \times 3 = 12\)
- \(12 \times 7 = 84\)
Thus, the least common multiple of 7 and 12 is \(84\).
The correct response is 84.
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