Example: 30 and 42
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Combine the factors, eliminating duplicates
2 x 3 x 5 x 7 = 210, the LCM
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You need at least two numbers to find a GCF.
You need at least two numbers to find an LCM no matter what you use.
Whatever you use, you need at least two numbers to find a GCF.
Divide prime numbers into it. Start with 2. Do that four times. Then try 3. Stop.
That is not what prime factorization is for.