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

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

• A. 12
• B. 24
• C. 8
• D. 10

Answer: (A)

To find the least common multiple (LCM) of two numbers, we seek the smallest multiple that both numbers share. In this case, we are looking at the numbers 4 and 6. First, let's list the multiples of both numbers: - The multiples of 4 are: 4, 8, 12, 16, 20, 24, etc. - The multiples of 6 are: 6, 12, 18, 24, etc. Now, we identify the multiples that these two lists have in common. The smallest number that appears in both lists is 12. Additionally, we can use prime factorization as another method to confirm this. The prime factorization of 4 is 2², and for 6, it is 2¹ × 3¹. To find the LCM, we take the highest power of each prime that appears in the factorizations: - For the prime number 2, the highest power is 2² from 4. - For the prime number 3, the highest power is 3¹ from 6. Thus, the LCM can be calculated as: LCM = 2² × 3¹ =

To find the least common multiple (LCM) of two numbers, we seek the smallest multiple that both numbers share. In this case, we are looking at the numbers 4 and 6.

First, let's list the multiples of both numbers:

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

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

Now, we identify the multiples that these two lists have in common. The smallest number that appears in both lists is 12.

Additionally, we can use prime factorization as another method to confirm this. The prime factorization of 4 is 2², and for 6, it is 2¹ × 3¹. To find the LCM, we take the highest power of each prime that appears in the factorizations:

• For the prime number 2, the highest power is 2² from 4.

• For the prime number 3, the highest power is 3¹ from 6.

Thus, the LCM can be calculated as:

LCM = 2² × 3¹ =