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

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

• A. 10
• B. 12
• C. 24
• D. 18

Answer: (B)

To determine the least common multiple (LCM) of 4 and 6, we first find the multiples of each number. The multiples of 4 are: 4, 8, 12, 16, 20, 24, etc. The multiples of 6 are: 6, 12, 18, 24, 30, etc. The LCM is defined as the smallest number that appears in both lists of multiples. Observing the multiples listed, the first number that appears in both sequences is 12. To confirm this, we can also use the prime factorization method. The prime factorization of 4 is \(2^2\), and for 6, it is \(2^1 \times 3^1\). To find the LCM, we take the highest power of each prime that appears in these factorizations. Thus, we take \(2^2\) from 4 and \(3^1\) from 6, which gives us: \[ LCM = 2^2 \times 3^1 = 4 \times 3 = 12 \] This value, 12, is indeed the

To determine the least common multiple (LCM) of 4 and 6, we first find the multiples of each number.

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

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

The LCM is defined as the smallest number that appears in both lists of multiples. Observing the multiples listed, the first number that appears in both sequences is 12.

To confirm this, we can also use the prime factorization method. The prime factorization of 4 is (2^2), and for 6, it is (2^1 \times 3^1). To find the LCM, we take the highest power of each prime that appears in these factorizations. Thus, we take (2^2) from 4 and (3^1) from 6, which gives us:

[

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

]

This value, 12, is indeed the