What is the least common multiple (LCM) of 3, 4, and 6?

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Multiple Choice

What is the least common multiple (LCM) of 3, 4, and 6?

Explanation:
To find the least common multiple (LCM) of 3, 4, and 6, we can start by determining the prime factorization of each number: - The prime factorization of 3 is \(3^1\). - The prime factorization of 4 is \(2^2\). - The prime factorization of 6 is \(2^1 \times 3^1\). Next, we identify the highest power of each prime number that appears in these factorizations: - For the prime number 2, the highest power is \(2^2\) (from 4). - For the prime number 3, the highest power is \(3^1\) (which appears in both 3 and 6). To find the LCM, we multiply the highest powers of the prime numbers together: \[ LCM = 2^2 \times 3^1 = 4 \times 3 = 12. \] Therefore, the least common multiple of 3, 4, and 6 is 12. This approach ensures that the LCM is the smallest number that can be evenly divided by all the original numbers. Each of 3,

To find the least common multiple (LCM) of 3, 4, and 6, we can start by determining the prime factorization of each number:

  • The prime factorization of 3 is (3^1).

  • The prime factorization of 4 is (2^2).

  • The prime factorization of 6 is (2^1 \times 3^1).

Next, we identify the highest power of each prime number that appears in these factorizations:

  • For the prime number 2, the highest power is (2^2) (from 4).

  • For the prime number 3, the highest power is (3^1) (which appears in both 3 and 6).

To find the LCM, we multiply the highest powers of the prime numbers together:

[

LCM = 2^2 \times 3^1 = 4 \times 3 = 12.

]

Therefore, the least common multiple of 3, 4, and 6 is 12.

This approach ensures that the LCM is the smallest number that can be evenly divided by all the original numbers. Each of 3,

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