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. 20
• D. 24

Answer: (D)

To determine the least common multiple (LCM) of 6 and 8, we start by finding the multiples of each number. The multiples of 6 are 6, 12, 18, 24, 30, etc., while the multiples of 8 are 8, 16, 24, 32, etc. The LCM is the smallest number that appears in both lists of multiples. In this case, the first common multiple of 6 and 8 is 24. Additionally, we can confirm this by using the prime factorization method. The prime factorization of 6 is \(2^1 \times 3^1\) and for 8, it is \(2^3\). To find the LCM, we take the highest power of each prime factor from both factorizations. Therefore, we take \(2^3\) from 8 and \(3^1\) from 6, which gives us \(LCM = 2^3 \times 3^1 = 8 \times 3 = 24\). Thus, the least common multiple of 6 and 8 is indeed 24.

To determine the least common multiple (LCM) of 6 and 8, we start by finding the multiples of each number. The multiples of 6 are 6, 12, 18, 24, 30, etc., while the multiples of 8 are 8, 16, 24, 32, etc. The LCM is the smallest number that appears in both lists of multiples.

In this case, the first common multiple of 6 and 8 is 24.

Additionally, we can confirm this by using the prime factorization method. The prime factorization of 6 is (2^1 \times 3^1) and for 8, it is (2^3). To find the LCM, we take the highest power of each prime factor from both factorizations. Therefore, we take (2^3) from 8 and (3^1) from 6, which gives us (LCM = 2^3 \times 3^1 = 8 \times 3 = 24).

Thus, the least common multiple of 6 and 8 is indeed 24.