What is the least common multiple of 6 and 28?(1 point)
Responses
168
168
4
4
84
84
2
168
To find the least common multiple (LCM) of 6 and 28, you can use the prime factorization method. Here are the steps:
Step 1: Find the prime factorization of each number.
- The prime factorization of 6 is 2 x 3.
- The prime factorization of 28 is 2 x 2 x 7.
Step 2: Determine the highest power of each prime factor.
- The highest power of 2 is 2 x 2.
- The highest power of 3 is 3.
- The highest power of 7 is 7.
Step 3: Multiply the highest power of each prime factor together.
2 x 2 x 3 x 7 = 84.
Therefore, the least common multiple of 6 and 28 is 84.
To find the least common multiple (LCM) of two numbers, like 6 and 28, you can use the following steps:
1. Prime factorize each number:
6 can be factored into 2 * 3
28 can be factored into 2^2 * 7
2. Identify the highest power for each prime factor:
- For the factor 2, the highest power is 2^2 (from 28).
- For the factor 3, the highest power is 3^1 (from 6).
- For the factor 7, the highest power is 7^1 (from 28).
3. Multiply the prime factors with their highest powers:
LCM = 2^2 * 3^1 * 7^1
4. Calculate the result:
LCM = 4 * 3 * 7 = 84
Therefore, the least common multiple (LCM) of 6 and 28 is 84.