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

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โˆ™ 2016-09-04 10:17:01
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Algebra

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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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Related questions

What is the greatest common multiple of 85 and 51?

There is no greatest common multiple of two numbers. For whatever number you come up with I can always add the lowest common multiple of the numbers to get an even higher common multiple.


True or False A common multiple of two numbers is always divisible by both the number?

True


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.


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.


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.


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 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.


Can two even numbers have a greatest common factor that is an odd number?

No. Because both numbers are even, they each have 2 as a factor. Even if they have a larger factor in common, it will be a multiple of 2, so the greatest common factor will be an even number.Yes. Two even numbers are each divisible by 2. The GCF must therefore always have two as one of its factors; this makes it even.


What is the greatest common multiple of 6 and 35?

The greatest common multiple of any set of integers is infinite.


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 is greatest common multiple?

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.


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 of 20 and 30?

There is no such word as multipul: it is multiple.Furthermore, 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 is the greatest common multiple of 51 and 85?

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.


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.


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 is it greatest common multiple?

The greatest common multiple isn't used because it can't be quantified. Since numbers don't stop, multiples don't stop either. The greatest common multiple for any set of integers is infinite.


What are two pairs of numbers with the given number as their greatest common multiple 8?

There is really so 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 is the greatest common multiple of 16 28 and 40?

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 is the greatest common multiple of 850?

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.Besides, the word "common" implies that the multiple is common to two or more numbers. There is only one number in the question.


What is greatest common?

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 is the greatest common multiple of 60 and 84?

There is really no such thing as a "greatest common multiple" (and certainly not "greatest common multiply"). 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 is the greatest common multiple of 26 and 48?

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 is the greatest common multiple of 140 and 25?

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.