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2 x 3 x 3 x 5 = 90

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13y ago

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What is it called when the product of a pair of numbers is the LCM also?

The numbers are relatively prime, or co-prime.


Is the product of 3 different prime numbers?

30 is the product of three different prime numbers.


How can you determine if the least common multiple of 2 numbers is the product of the 2 numbers or less than the product of the 2 numbers?

If the GCF of a given pair of numbers is 1, the LCM will be equal to their product. If the GCF is greater than 1, the LCM will be less than their product. Or, stated another way, if the two numbers have no common prime factors, their LCM will be their product.


Is the product of two prime numbers is always composite?

Yes, it is always. Assume temporarily that the product of two prime numbers is not always composite. This implies that that at least one product of prime numbers is also prime. Now, say two different prime numbers p and q, when multiplied, equal r. If r is a prime number, then r's only positive factors are 1 and r. But 1 is not a prime number. This contradicts that both p and q are prime (because either p or q MUST be 1). Therefore, the product of two prime numbers is always composite.


Is the LCM of two numbers that have no common factors their product?

The LCM of two numbers is one of the numbers when one of the numbers is a multiple of the other. The LCM of two numbers is the product of the numbers when they are relatively prime. In all other cases (like consecutive even numbers that aren't 2 and 4) the LCM is as you describe.