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Q: How can determine from the prime factorizations wheather the least common multiple of two numbers of the product of numbers or is less then the product of two numbers?

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If the prime factorizations have no factors in common, the LCM is the product of them.

If none of the prime factors are in common, the LCM will be the product of the two.

Comparing their prime factorizations is a fast and easy way to determine their greatest common factor and their least common multiple.

If there are no prime factors in common, the LCM will be the product. If there are prime factors in common, the LCM will be less than the product.

If the prime factorizations have no prime factors in common, the numbers are relatively prime.

Since prime numbers only have one prime factor (themselves), they don't have prime factorizations.

If there are no common prime factors, the GCF is 1.

Use the prime factorizations to determine the GCF. If the GCF is 1, the numbers are relatively prime. If the two numbers have no prime factors in common, they are relatively prime.

If the prime factorizations contain no factors in common (their GCF is 1), the numbers are relatively prime.

If the two numbers have no common factors (other than 1), then the LCM is equal to the product of the two numbers. If they have some factors in common, then those factors need only be used once when multiplying, so the LCM will be less than the product of the two numbers.

If there are no prime factors in common, the LCM will be the product of the two numbers. If common factors exist, the LCM will be less. It will never be more.

Only composite numbershave prime factorizations. Prime factorizations must consist of only prime numbers.

At least two.

Negative numbers don't have prime factorizations.

5 and 11, as prime numbers, don't have prime factorizations. Their LCM is their product.

You can do prime factorization with probably every numbers. You have to be specific about the numbers you want to know.

Negative numbers do not have prime factorizations.

This cannot be properly answered because at least two numbers are needed to determine the common multiple.

This cannot be properly answered because at least two numbers are needed to determine the common multiple.

No, prime factorizations consist entirely of prime numbers.

Prime factorizations are expressions of numbers as products of prime factors. The prime factorization of 30 is 2 x 3 x 5.

Negative numbers don't have prime factorizations.

Negative numbers don't have prime factorizations.

Negative numbers don't have prime factorizations.

Negative numbers don't have prime factorizations.