What is the least common multiple (LCM) of 6 and 8?

What is the least common multiple (LCM) of 6 and 8?

• A. 12
• B. 18
• C. 24
• D. 30

Answer: (C)

To determine the least common multiple (LCM) of 6 and 8, we start by identifying the prime factors of each number. 6 can be factored into prime numbers as: 6 = 2 × 3. 8 can be factored into prime numbers as: 8 = 2 × 2 × 2, or 2^3. The next step in finding the LCM is to take the highest power of each prime factor present in the factorizations. The prime factors involved are 2 and 3. - For the prime factor 2, the highest power between the two factorizations is 2^3 from 8. - For the prime factor 3, the highest power is 3^1 from 6. Thus, to calculate the LCM, you multiply these highest powers together: LCM = 2^3 × 3^1 = 8 × 3 = 24. Therefore, the least common multiple of 6 and 8 is indeed 24, confirming that the correct answer is accurate.

To determine the least common multiple (LCM) of 6 and 8, we start by identifying the prime factors of each number.

6 can be factored into prime numbers as:

6 = 2 × 3.

8 can be factored into prime numbers as:

8 = 2 × 2 × 2, or 2^3.

The next step in finding the LCM is to take the highest power of each prime factor present in the factorizations. The prime factors involved are 2 and 3.

• For the prime factor 2, the highest power between the two factorizations is 2^3 from 8.

• For the prime factor 3, the highest power is 3^1 from 6.

Thus, to calculate the LCM, you multiply these highest powers together:

LCM = 2^3 × 3^1 = 8 × 3 = 24.

Therefore, the least common multiple of 6 and 8 is indeed 24, confirming that the correct answer is accurate.