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Q: Do two natural numbers always have a least common multiple?

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No, not always.

Yes, the least common multiple of two numbers is always divisible by those numbers' greatest common factor.

No. You can always find a common multiple by multiplying two numbers together. It will only be the least common multiple if the numbers have no common factors other than one.

Yes.

yes

There is no greatest common multiple of two numbers. For whatever number you come up with I can always add the lowest common multiple of the numbers to get an even higher common multiple.

A number is an exact multiple of each of a group of numbers. For example, 15 and 30 are common multiple of 3 and 5.

Yes - if two numbers share no common factors (besides 1) the least common multiple will be the product of the numbers.

Sometimes, not always.

The product of all pairs of prime numbers is always the least common multiple of the two prime numbers.

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Sometimes, not always.

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