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

• A. 24
• B. 12
• C. 18
• D. 48

Answer: (A)

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

For 6, the prime factors are:

• (6 = 2 \times 3)

For 8, the prime factors are:

• (8 = 2^3)

To find the LCM, we take the highest power of each prime factor that appears in the factorizations. This involves both identifying the primes and their maximum powers:

• The prime 2 appears in both factorizations. The maximum power of 2 is (2^3) from 8.

• The prime 3 appears only in the factorization of 6 as (3^1).

Now, we multiply these highest powers together to find the LCM:

• LCM = (2^3 \times 3^1 = 8 \times 3 = 24)

Hence, the least common multiple of 6 and 8 is 24. This confirms that the provided answer is accurate, as 24 is indeed the smallest number that both 6 and 8 divide into without a remainder.