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. 36
• D. 48

Answer: (A)

To determine the least common multiple (LCM) of two numbers, you can use the method of listing the multiples of each number or by finding the prime factorization. For the numbers 4 and 6, we first identify their multiples: - The multiples of 4 are: 4, 8, 12, 16, 20, 24, ... - The multiples of 6 are: 6, 12, 18, 24, 30, ... The LCM is the smallest multiple that appears in both lists. From the lists above, the first common multiple is 12. Therefore, the least common multiple of 4 and 6 is 12. Alternatively, using prime factorization: - The prime factorization of 4 is \(2^2\). - The prime factorization of 6 is \(2^1 \times 3^1\). To find the LCM using prime factors, you take the highest power of each prime number that appears in the factorizations. For 2, the highest power is \(2^2\) (from 4), and for 3, it is \(3^1\) (from 6). Thus,

To determine the least common multiple (LCM) of two numbers, you can use the method of listing the multiples of each number or by finding the prime factorization.

For the numbers 4 and 6, we first identify their multiples:

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

• The multiples of 6 are: 6, 12, 18, 24, 30, ...

The LCM is the smallest multiple that appears in both lists. From the lists above, the first common multiple is 12. Therefore, the least common multiple of 4 and 6 is 12.

Alternatively, using prime factorization:

• The prime factorization of 4 is (2^2).

• The prime factorization of 6 is (2^1 \times 3^1).

To find the LCM using prime factors, you take the highest power of each prime number that appears in the factorizations. For 2, the highest power is (2^2) (from 4), and for 3, it is (3^1) (from 6). Thus,