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. 18

Answer: (A)

To find the least common multiple (LCM) of 4 and 6, you first list the multiples of each number: Multiples of 4: 4, 8, 12, 16, 20, 24, ... Multiples of 6: 6, 12, 18, 24, ... The LCM is the smallest multiple that is common to both lists. By examining the multiples, the first number that appears in both lists is 12. This indicates that 12 is a common multiple. To further solidify this, you can use the prime factorization method. The prime factorization of 4 is \(2^2\), and for 6, it is \(2^1 \times 3^1\). For the LCM, you take the highest power of each prime number from both factorizations: - For the prime number 2, the highest power present is \(2^2\). - For the prime number 3, the highest power present is \(3^1\). Now, you multiply these together: \(LCM = 2^2 \times 3^1 = 4 \times 3 = 12

To find the least common multiple (LCM) of 4 and 6, you first list the multiples of each number:

Multiples of 4: 4, 8, 12, 16, 20, 24, ...

Multiples of 6: 6, 12, 18, 24, ...

The LCM is the smallest multiple that is common to both lists. By examining the multiples, the first number that appears in both lists is 12. This indicates that 12 is a common multiple.

To further solidify this, you can use the prime factorization method. The prime factorization of 4 is (2^2), and for 6, it is (2^1 \times 3^1). For the LCM, you take the highest power of each prime number from both factorizations:

• For the prime number 2, the highest power present is (2^2).

• For the prime number 3, the highest power present is (3^1).

Now, you multiply these together:

(LCM = 2^2 \times 3^1 = 4 \times 3 = 12