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

Updated: 4/28/2022 Wiki User

7y ago

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

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

### 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.

### What is the greatest common multiple of 85 and 51?

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.

### 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 sum of two consecutive numbers always divisible by 2?

No, the sum of two consecutive numbers is always an odd number, and is not divisible by two.

### What is the greatest common multiple for any two numbers?

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.

### Can two whole numbers have a greatest common multiple?

No, 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.

### What numbers have 90 as a greatest common multiple?

There is really no such thing as a "greatest common multiple". Once you find the least common multiple (LCM) 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.

### What are two numbers that have 5 as their greatest common multiple?

There are no such numbers because there is really no such thing as a "greatest common multiple". If the numbers have 5 as a common multiple then 10 will also be a common multiple and clearly, 10 is greater than 5. So 5 cannot be the greatest common multiple. In fact, 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.

### 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.