What is the least common multiple of 4 and 6?

To find the least common multiple (LCM) of two numbers, we start by identifying the multiples of each number and then find the smallest multiple shared by both.

The multiples of 4 are:

4, 8, 12, 16, 20, 24, 28, 32, ...

The multiples of 6 are:

6, 12, 18, 24, 30, 36, ...

From these two lists, we can see that the smallest multiple that appears in both is 12. Therefore, 12 is the least common multiple of 4 and 6.

Another way to determine the LCM is to use the prime factorization method. The prime factorization of 4 is 2^2, and for 6 it is 2^1 × 3^1. To find the LCM, we take the highest power of each prime present in the factorizations:

• The highest power of 2 from both numbers is 2^2.

• The highest power of 3 is 3^1.

Thus, the LCM is calculated as follows:

LCM = 2^2 × 3^1 = 4 × 3 =