You multiply numbers because you're trying to find a multiple. You multiply prime numbers because you're trying to find the smallest common number. You could multiply common composite factors, but the result wouldn't necessarily be least.
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Multiply them together.
What you do is multiply all 3 numbers together.
When all of them are prime numbers,then just multiply the numbers to get the LCM of those 3 numbers.
Product = multiply.
There is no need to do prime factorization as prime numbers are already prime. You do not need to find the prime numbers that when multiplied together create the number.