Best Answer

The prime factorization of the LCM will contain all the prime factors of the two original numbers. When the original numbers don't have any prime factors in common, (the GCF is 1) the LCM will be their product. When the two original numbers have prime factors in common (the GCF is 2 or more) the duplicates will be discarded and the LCM will be less than their product.

Q: Why do you think the least common multiple is not always the product of the two numbers?

Write your answer...

Submit

Still have questions?

Continue Learning about Basic Math

Not always. The product of two numbers will always be a common multiple, but it will not always be least. The product of 4 and 9 is 36. The LCM of 4 and 9 is 36. The product of 4 and 8 is 32. The LCM of 4 and 8 is 16.

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

The least common factor for two numbers is always one. The least common multiple for two numbers which have no common factors greater than one is their product.

Their product.

The least common multiple of two different prime numbers is the product of those two prime numbers.

Related questions

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

No, only if the numbers are relatively prime.

yes

Sometimes, not always.

Yes.

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

Yes, the least common multiple is the product of the two numbers or the lowest number that both multiples can go into.

Yes, as long as the numbers are positive.

No, this will find a common multiple, but not always the least. For example, 2 and 4 have a least common multiple of 4 but if you multiply them you get 8. In fact, the LCM will only be the product of two numbers if the numbers have no common factors. We call numbers with no common factors relatively prime.

7 times 23. The product of 2 numbers is always a common multiple but not necessarily the least. Question for you : When is the LCM the product ? Think about the relation between the product, the LCM and the Greatest Common Factor.

Not always. The product of two numbers will always be a common multiple, but it will not always be least. The product of 4 and 9 is 36. The LCM of 4 and 9 is 36. The product of 4 and 8 is 32. The LCM of 4 and 8 is 16.

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