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Q: Is the product of two numbers always a common multiple of those numbers?

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No, not always.

yes

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

Sometimes, not always.

Sometimes, not always.

Yes.

No, only if the numbers are relatively prime.

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

Multiplying two numbers together will create a common multiple. It is sometimes, but not always, the LCM as well.

Yes, as long as the numbers are positive.

It's always a common multiple; it's not always least. Simple counter example: 4 × 6 = 24 But LCM(4, 6) = 12 ------------------------------------------------------------------------------------ Note: HCF(4, 6) = 2 What is true of any two whole numbers that the product of the two numbers is equal to the product of their highest common factor and lowest common multiple. eg 4 × 6 = hcf(4, 6) × lcm(4, 6) = 2 × 12 = 24.

Never. The greatest common multiple of any two numbers is infinite.

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