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No. Counter Example: -2 * -2 = 4
A product is the answer to two multiplication problems. Example: 2*2=4 / product
Product of the two prime numbers is the LCM. For example 3, 7 have 21 as LCM
If by "opposite" you mean "additive inverse", then yes.
If the two numbers do not have any factors in common (other than 1), then the LCM is the same as the product of the two numbers. Example: LCM of 5 & 6 is 30, which is the same as the product.