Find the least common multiple of 7 and 12.(1 point)

Question

Responses

252
252

48
48

84
84

168

Answer 1

To find the least common multiple (LCM) of 7 and 12, we can use the prime factorization method.

1. Prime factorization:

   • The prime factorization of 7 is simply \( 7^1 \).
   • The prime factorization of 12 is \( 2^2 \times 3^1 \).

2. 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 \( 7^1 \).

3. 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