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