What is the least common multiple of 4 and 6?

What is the least common multiple of 4 and 6?

• A. 12
• B. 18
• C. 24
• D. 30

Answer: (A)

To find the least common multiple (LCM) of two numbers, we start by identifying the multiples of each number and then find the smallest multiple shared by both. The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, ... The multiples of 6 are: 6, 12, 18, 24, 30, 36, ... From these two lists, we can see that the smallest multiple that appears in both is 12. Therefore, 12 is the least common multiple of 4 and 6. Another way to determine the LCM is to use the prime factorization method. The prime factorization of 4 is 2^2, and for 6 it is 2^1 × 3^1. To find the LCM, we take the highest power of each prime present in the factorizations: - The highest power of 2 from both numbers is 2^2. - The highest power of 3 is 3^1. Thus, the LCM is calculated as follows: LCM = 2^2 × 3^1 = 4 × 3 =

To find the least common multiple (LCM) of two numbers, we start by identifying the multiples of each number and then find the smallest multiple shared by both.

The multiples of 4 are:

4, 8, 12, 16, 20, 24, 28, 32, ...

The multiples of 6 are:

6, 12, 18, 24, 30, 36, ...

From these two lists, we can see that the smallest multiple that appears in both is 12. Therefore, 12 is the least common multiple of 4 and 6.

Another way to determine the LCM is to use the prime factorization method. The prime factorization of 4 is 2^2, and for 6 it is 2^1 × 3^1. To find the LCM, we take the highest power of each prime present in the factorizations:

• The highest power of 2 from both numbers is 2^2.

• The highest power of 3 is 3^1.

Thus, the LCM is calculated as follows:

LCM = 2^2 × 3^1 = 4 × 3 =