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

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

• A. A) 24
• B. B) 8
• C. C) 12
• D. D) 18

Answer: (C)

To find the least common multiple (LCM) of two numbers, you need to determine the smallest multiple that both numbers share. For 4 and 6, you can list their multiples or use prime factorization. The multiples of 4 are: 4, 8, 12, 16, 20, 24, ... The multiples of 6 are: 6, 12, 18, 24, ... The smallest number that appears in both lists of multiples is 12, making it the least common multiple of 4 and 6. In terms of prime factorization, you can express 4 as \(2^2\) and 6 as \(2^1 \times 3^1\). To find the LCM, take the highest power of each prime that appears in the factorizations. This gives you \(2^2\) from 4 and \(3^1\) from 6. When you multiply these together, you get \(2^2 \times 3^1 = 4 \times 3 = 12\). Therefore, the LCM of 4 and 6 is 12, confirming that the choice of 12 is correct

To find the least common multiple (LCM) of two numbers, you need to determine the smallest multiple that both numbers share. For 4 and 6, you can list their multiples or use prime factorization.

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

The multiples of 6 are: 6, 12, 18, 24, ...

The smallest number that appears in both lists of multiples is 12, making it the least common multiple of 4 and 6.

In terms of prime factorization, you can express 4 as (2^2) and 6 as (2^1 \times 3^1). To find the LCM, take the highest power of each prime that appears in the factorizations. This gives you (2^2) from 4 and (3^1) from 6. When you multiply these together, you get (2^2 \times 3^1 = 4 \times 3 = 12).

Therefore, the LCM of 4 and 6 is 12, confirming that the choice of 12 is correct