What is the least common multiple (LCM) of 8 and 12?

What is the least common multiple (LCM) of 8 and 12?

• A. 24
• B. 36
• C. 48
• D. 60

Answer: (A)

To find the least common multiple (LCM) of 8 and 12, we start by determining the prime factorization of both numbers. For 8, the prime factorization is \(2^3\) since \(8 = 2 \times 2 \times 2\). For 12, the prime factorization is \(2^2 \times 3\) because \(12 = 2 \times 2 \times 3\). The LCM is found by taking the highest powers of all prime factors present in the factorizations. - For the prime factor 2, the highest power in our factorizations is \(2^3\) (from 8). - For the prime factor 3, the highest power is \(3^1\) (from 12). Now we multiply these highest powers together to find the LCM: \[ LCM = 2^3 \times 3^1 = 8 \times 3 = 24. \] Thus, the least common multiple of 8 and 12 is 24. This makes the correct answer 24, which aligns with the choice provided.

To find the least common multiple (LCM) of 8 and 12, we start by determining the prime factorization of both numbers.

For 8, the prime factorization is (2^3) since (8 = 2 \times 2 \times 2).

For 12, the prime factorization is (2^2 \times 3) because (12 = 2 \times 2 \times 3).

The LCM is found by taking the highest powers of all prime factors present in the factorizations.

• For the prime factor 2, the highest power in our factorizations is (2^3) (from 8).

• For the prime factor 3, the highest power is (3^1) (from 12).

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

[

LCM = 2^3 \times 3^1 = 8 \times 3 = 24.

]

Thus, the least common multiple of 8 and 12 is 24. This makes the correct answer 24, which aligns with the choice provided.