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Well, not always. The GCF and LCM of 10 and 10 is 10. But apart from that special circumstance, the statement is true. Apart from a number itself, all of its factors are smaller than it. Apart from a number itself, all of its multiples are larger than it. You can't have a GCF that is greater than the smaller number, and you can't have an LCM that is less than the larger one which means that the LCM of two numbers will never be less than the GCF. Factors go into numbers, numbers go into multiples.

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A common factor of two numbers is a factor of both numbers.

The largest factor that a number has is itself, so the greatest factor that the

smaller number can have is itself. If it is a factor of the larger number then it would

be the greatest common factor. If not , the greatest common factor would have to be

smaller.

The least common factor of any set of integers is 1. If the numbers are co-prime, then the greatest common factor will also be 1 and thus the least and greatest common factors will be the same.

Because a number can't have a factor larger than itself.

The product of two numbers is equal to the product of their GCF and their LCM. Divide the original product by one of them, you will get the other.

If the divisor was larger than one of the numbers, it couldn't be a divisor. There is no factor of a number that is larger than the number.

Because they have no other common factors that are greater.

Only when one of the numbers is a factor of the other.

No, the greatest of the common factors of two or more numbers is the greatest common factor, or GCF. The least common factor of two or more numbers is 1.

Only if that number is a factor of the other.

Q: Is the greatest common factor of two numbers is equal to the lesser of the number?

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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).

I can't give you an example of when that happens because that doesn't ever happen. The GCF of a pair of numbers can't be larger than the smaller number.

Let's try one. 30x2y3z4 + 42x4y5z2 Do the numbers first. Factor them. 2 x 3 x 5 = 30 2 x 3 x 7 = 42 Combine the factors, eliminating duplicates. 2 x 3 x 5 x 7 = 210 For the variables, select the highest exponent. The LCM of the above expression is 210x4y5z4

False

As a general rule, multiples tend to be larger than factors. This is not always true. 9 is a factor of 27. 6 is a multiple of 3. The important distinction is in the relationship to the number they are factors or multiples of. A factor will be equal to or lesser than the number. A multiple will be equal to or greater than the number.

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No, the lesser.

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Given a pair of numbers, if the lesser of the two is the GCF, the greater of the two is the LCM. This happens when one of the numbers is a factor of the other.

If one number is a factor of another number, the greatest common factor will be the lesser number. Example: 3 and 9 3 is a factor of 9 3 is a factor of 3 There can be no higher factor of a number than the number itself. Therefore, the GCF of 3 and 9 is 3.

When that number is a factor of the greater one.

Only if that number is a factor of the other one.

Consider this:If A can be split into AB, where B is the lesser number (factor), then it can divide in. Thus, the GCF of the 2 numbers must be the lesser number, so that is true.

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).

If it isn't, then it can't be. The GCF of any two positive integers can never be greater than the lesser number.

When one of the numbers is a multiple of the other, the greater is the LCM and the lesser is the GCF of that set.

I can't give you an example of when that happens because that doesn't ever happen. The GCF of a pair of numbers can't be larger than the smaller number.

No, it's never greater than the lesser number.