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# When a number is a multiple of another the greatest common factor of the numbers is the greater of the numbers?

Updated: 8/29/2023

Wiki User

7y ago

If the GCF of two numbers is 1, their LCM will be their product. Such numbers are called relatively prime, or co-prime. Any two prime numbers (like 3 and 5) will be that way, but the numbers don't have to be prime (like 4 and 9).

Wiki User

6y ago

Wiki User

11y ago

That happens when one of the numbers is a multiple of the other.

Wiki User

8y ago

The LCM of two numbers will never be less than the GCF.

Wiki User

8y ago

In that scenario, the GCF is the lesser of the numbers. The LCM is the greater.

Wiki User

6y ago

Not necessarily. The LCM of 12 and 6 is 12. It's better to say the LCM of two numbers is never less than the greater of the two.

Wiki User

7y ago

No, the GCF is the lesser of the numbers.

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Q: When a number is a multiple of another the greatest common factor of the numbers is the greater of the numbers?
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No, the lesser.

### When a number is a multiple of another the GCF of the numbers is the greatest common factor?

The GCF of the numbers is the greatest common factor no matter what their relationship is. When one number is a multiple of another number, the GCF is the smaller number.

### What is the greatest common multiple of 7?

There can never be a greatest common multiple of one number for two reasons:"Common" refers to a multiple that is common to two or more numbers. You cannot have a multiple that is common, but only to one number.If X is the greatest common multiple of a set of numbers, then any multiple of X will also be a common multiple of each member of the set and it will be greater than X. And then, any multiple of this number will be a multiple of each member of the set and will be greater still. And then ...

### What is the greatest common multiple of 3 and 5?

There is no greatest common multiples for whatever common multiple is claimed to be the greatest the lowest common multiple of the numbers (in this case 15) can be added to get an even greater common multiple.

### 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 24 and 52?

There is no greatest common multiple of any integers as whatever number is said to be it, the lowest common multiple of the numbers can be added to get an even greater common multiple. If you mean least common multiple (the lowest (positive) integer that can be divided by the numbers without a remainder), the answer is 312. If you mean the greatest common factor (the greatest (positive) integer that can divide into the numbers without any remainder). the answer is 4.

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

There is no "greatest common multiple" of any two numbers. Whatever their product is, it can be multiplied by any positive integer to yield an even greater number that is also a multiple of the first two. Thus, the number of multiples is infinite.

### Can two even numbers have a greatest common multiple of 1?

The greatest common multiple of any set of numbers is infinite. The greatest common multiple of any set of numbers will never be one.

### Can you find the greatest common multiple of two numbers?

The greatest common multiple of any two numbers is infinite.

### What is the greatest denominator for 4 and 19?

There can be no greatest denominator. Suppose x is the greatest denominator of two numbers a and b. That is to say, x is a multiple of a, x is a multiple of b and x is the greatest such number. Now consider the number 2x. It is a multiple of a, it is a multiple of b and it is greater than x. This contradicts the statement that x is the greatest such number. So such an x cannot exist.

### 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.

### 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.