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Q: What will the prime factorization of this multiple have in common with the prime factorizations of 72?

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

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

prime factorizations:2x2x7

Negative numbers do not have prime factorizations.

All multiples of 36 contain the prime factorization of 36.

Prime factorization of 40 = 2x2x2x5 Prime factorization of 100 = 2x2x5x5

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

103 is already prime, no need for a factorization.

Variables don't have prime factorizations.

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Negative numbers don't have prime factorizations.

Negative numbers don't have prime factorizations.

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