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

Updated: 4/28/2022

Wiki User

11y ago

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.

Wiki User

11y ago

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

### When the greatest common factor is 1 is the least common multiple of these numbers always the product of the numbers?

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

### Is the product always the least common multiple of the numbers?

No, only if the numbers are relatively prime.

yes

### Is the least common multiple of any two numbers their product?

Sometimes, not always.

Yes.

### Are there any pairs of prime numbers that when multiplied do not make their least common multiple?

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

### Is the LCM of two numbers their product?

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

### Is it always true that if you divide the product of two numbers by the Greatest common factor you find the Least common multiple?

Yes, as long as the numbers are positive.

### Can you always find the LCM for two numbers by muiltiplying them together?

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.

### What is the least common multiple of 7 and 23?

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.

### Is the LCM of two numbers the product of the two numbers explain in words?

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.

### When is the product of two numbers divided by the greatest common multiple the least common multiple?

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