What is the least common multiple of 4 and 6?

To find the least common multiple (LCM) of two numbers, we can use the prime factorization approach or list the multiples of each number until we find the smallest common one.

First, consider the prime factorizations:

• The number 4 can be factored into (2^2).

• The number 6 can be factored into (2^1 \times 3^1).

To find the LCM, we take the highest power of each prime factor that appears in the factorizations. Here, we have:

• The highest power of 2 is (2^2) (from 4).

• The highest power of 3 is (3^1) (from 6).

Now, we multiply these together:

[

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

]

Thus, the least common multiple of 4 and 6 is 12. This number is also the smallest one that is a multiple of both, confirming that it is indeed the correct answer.

To further illustrate, if we check the multiples:

• The multiples of 4 are 4, 8,