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

Updated: 9/20/2023

Wiki User

12y ago

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

Wiki User

12y ago

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

### Is the least common multiple of two numbers always divisible by the greatest common factor of the two numbers?

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

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

No, only if the numbers are relatively prime.

yes

### 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.

### What is the least common multiple of 11 and 23?

The LCM or least common multiple is 253. In this case, the greatest common factor of the two numbers is 1. That is to say, they have no other common factors. We call these numbers relatively prime. When two numbers are relatively prime their LCM is always the product of the two numbers.Sometimes it is easier to find the greatest common factor than to find the least common multiple by looking at multiples of both numbers. This is true if the numbers are primes like 11 and 23. So if you are give two primes, the LCM will always be the product of the two numbers.

### When one number is a multiple of another the gcf of the numbers is always sometimes or never the greatest of the numbers?

The answer is sometimes - when the multiple in question is 1.

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

Sometimes, not always.

Yes.

### What is the greatest common multiple of 8 and 13?

There is really no such thing as a "greatest common multiple". Once you find the least common multiple of a set of numbers, you can keep adding the LCM to itself over and over again. Each new number you get will be a common multiple of your set of numbers, but each new number will always be larger than the previous. This means that you can keep adding while the number approaches infinity and you will still never find a greatest multiple.

### How can you find a greatest common multiple by using a factor tree?

Trees aren't necessary. The greatest common multiple of any set of numbers is always infinite.

### What is the greatest common multiple of 11and 17?

Greatest common multiple of two prime numbers is always 1. Therefore, gcf of 11 and 17 is 1.