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

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Multiple Choice

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

Explanation:
To find the least common multiple (LCM) of 4 and 6, we first identify the multiples of each number. The multiples of 4 are: 4, 8, 12, 16, 20, 24, and so on. The multiples of 6 are: 6, 12, 18, 24, 30, and so on. Next, we look for the smallest multiple that appears in both lists. By comparing the two sets of multiples, we see that 12 is the first multiple that both 4 and 6 share. We can also use the prime factorization method to confirm this. The prime factorization of 4 is \(2^2\) and for 6 it is \(2^1 \times 3^1\). To determine the LCM, we take the highest power of each prime number present in the factorizations: - For the prime number 2, the highest power is \(2^2\) (from 4). - For the prime number 3, the highest power is \(3^1\) (from 6). Multiplying these together gives us: \[ LCM = 2^

To find the least common multiple (LCM) of 4 and 6, we first identify the multiples of each number.

The multiples of 4 are: 4, 8, 12, 16, 20, 24, and so on.

The multiples of 6 are: 6, 12, 18, 24, 30, and so on.

Next, we look for the smallest multiple that appears in both lists. By comparing the two sets of multiples, we see that 12 is the first multiple that both 4 and 6 share.

We can also use the prime factorization method to confirm this. The prime factorization of 4 is (2^2) and for 6 it is (2^1 \times 3^1). To determine the LCM, we take the highest power of each prime number present in the 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) (from 6).

Multiplying these together gives us:

[

LCM = 2^

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