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

To find the least common multiple (LCM) of 4 and 6, we can begin by identifying the multiples of each number.

The multiples of 4 are: 4, 8, 12, 16, 20, 24, and so on.

The multiples of 6 are: 6, 12, 18, 24, 30, and so on.

Next, we look for the smallest multiple that appears in both lists. The first multiple that appears in both lists is 12. This means that 12 is the first number that can be divided evenly by both 4 and 6, making it the least common multiple.

Furthermore, we can confirm this by using the prime factorization method:

• 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, we take the highest power of each prime:

• For the prime number 2, the maximum exponent from both factorizations is 2.

• For the prime number 3, the maximum exponent is 1.

Thus, the LCM can be calculated as