How to do (LCM) and (GCF) with prime factorization

Sure, here's how you can find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) using prime factorization:

1. Prime Factorization: This is the process of finding the prime numbers that multiply together to make a certain number. For example, the prime factorization of 12 is 223.

Step by Step Process for LCM:

1. Write down the prime factorization of each number. For example, if you're finding the LCM of 12 and 15, you would write 223 (for 12) and 3*5 (for 15).

2. Identify the common factors. In this case, the common factor is 3.

3. For the LCM, take all the prime factors from both numbers, but only repeat common factors once. So, for 12 and 15, you would have 2, 2, 3, and 5.

4. Multiply these factors together to get the LCM. So, 223*5 = 60. Therefore, the LCM of 12 and 15 is 60.

Step by Step Process for GCF:

1. Write down the prime factorization of each number, just like you did for the LCM.

2. Identify the common factors. Again, in the case of 12 and 15, the common factor is 3.

3. For the GCF, you only take the common factors. So, for 12 and 15, you would only take 3.

4. Multiply these factors together to get the GCF. So, in this case, the GCF is just 3, because 3 is the only common prime factor of 12 and 15.

Remember, the LCM will always be a multiple of the GCF.