Yes - if two numbers share no common factors (besides 1) the least common multiple will be the product of the numbers.
Their product as for example LCM of 3 and 7 is 21
Never. The greatest common multiple of any two numbers is infinite.
Multiply any two numbers together. Their product will be a common multiple of the two.
If the least common multiple of two numbers equals the product of the two numbers, then the numbers are relatively prime, that is their highest common factor is 1. For example, the numbers 10 and 21: The lcm is 10 x 21 = 210 They are relatively prime since their hcf is 1.
No, not always.
If the prime factorizations have no numbers in common, the LCM is their product.