What is the process to find the least common multiple (LCM) using prime factors?

To find the least common multiple (LCM) using prime factors, the correct process involves identifying all the prime factors that appear in either of the numbers you are working with. After you have obtained the prime factorization of each number, you must list all the unique prime factors, which includes both those that are common to the numbers and those that are unique to each number.

Once you have this complete list of unique prime factors, you multiply these together. Additionally, for each prime factor that appears in the prime factorization of the numbers, you must include it as many times as it has the highest count from either number. This ensures that the LCM is the smallest number that is a multiple of both original numbers.

The other processes mentioned do not align with the proper method to find the LCM. Simply listing the prime factors and multiplying them together does not account for the necessary repetitions of prime factors, and multiplying prime factors that appear more than once would mean not fully recognizing their contribution to the LCM. Meanwhile, finding the greatest factor of both numbers is a method used to determine the greatest common divisor (GCD), which is fundamentally different from finding the LCM.