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. 6
• D. 2

Answer: (A)

The least common multiple (LCM) of two numbers is the smallest multiple that is evenly divisible by both numbers. To find the LCM of 4 and 6, we can start by listing the multiples of each number. The multiples of 4 are: 4, 8, 12, 16, 20, 24, ... The multiples of 6 are: 6, 12, 18, 24, ... Next, we look for the smallest number that appears in both lists. Observing the lists, the number 12 is the first multiple that both 4 and 6 have in common. This makes 12 the least common multiple. Alternatively, the LCM can also be found using the prime factorization method: - The prime factorization of 4 is 2². - The prime factorization of 6 is 2¹ × 3¹. To calculate the LCM using prime factors, take the highest power of each prime number that appears in the factorizations: - The highest power of 2 is 2². - The highest power of 3 is 3¹. Now, multiply these together: 2² × 3¹ = 4 × 3

The least common multiple (LCM) of two numbers is the smallest multiple that is evenly divisible by both numbers. To find the LCM of 4 and 6, we can start by listing the multiples of each number.

The multiples of 4 are:

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

The multiples of 6 are:

6, 12, 18, 24, ...

Next, we look for the smallest number that appears in both lists. Observing the lists, the number 12 is the first multiple that both 4 and 6 have in common. This makes 12 the least common multiple.

Alternatively, the LCM can also be found using the prime factorization method:

• The prime factorization of 4 is 2².

• The prime factorization of 6 is 2¹ × 3¹.

To calculate the LCM using prime factors, take the highest power of each prime number that appears in the factorizations:

• The highest power of 2 is 2².

• The highest power of 3 is 3¹.

Now, multiply these together:

2² × 3¹ = 4 × 3