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The LCM will never be less than the GCF. To be a multiple of both numbers, the LCM will have to be equal to or greater than the larger number. To be a factor of both numbers, the GCF will have to be equal to or less than the smaller number.

The only problem comes when you're comparing a number to itself. The LCM of 10 and 10 is 10. The GCF of 10 and 10 is 10.

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โˆ™ 2017-09-19 15:20:26
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โˆ™ 2017-09-15 12:44:51

The LCM is at least as great. The LCM is a multiple of the two numbers and so must be at least as large as the two numbers. Consequently it must be at least as large as the larger of the two numbers. On the other hand, the GCF is a factor of the two numbers and so must be at most as large as the two numbers. Consequently it must be at most as large as the smaller of the two numbers. Combining these inequalities shows that the LCM must be at least as great as the GCF.

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Q: How Given any two numbers which is greater the LCM of the numbers or. The GCF of the numbers why?
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Related questions

If given any two numbers which is greater the LCM of the numbers or the GCF of the numbers?

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


Is greater the LCM of the numbers or the numbers or the GCF of the numbers?

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


What is greater LCM or GCF?

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


Is GCF greater or is LCM?

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


Which is greater gcf or LCM?

The LCM of a set of numbers will never be less than their GCF.


When one number is a multiple of another the gcf of the number is the greater of the numbers?

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


Which is greater the GCF of a number or the LCM of a number?

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


Which is greater the LCM of the number or GCF of the number?

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


What is the GCF and the LCM of 1570?

To find the GCF and LCM at least two or more numbers must be given


When is the LCM not the product of the two numbers?

When their GCF is greater than one.


For a given pair of numbers how can you tell whether the least common multiple will be less than or equal to their product?

If the GCF of a given pair of numbers is 1, the LCM will be equal to their product. If the GCF is greater than 1, the LCM will be less than their product. Or, stated another way, if the two numbers have no common prime factors, their LCM will be their product.


How can yo determine whether the LCM of two numbers is the product of the numbers or less than the product of the numbers?

If their GCF is 1, their LCM is their product. If their GCF is greater than 1, their LCM is less than their product.


What pair of numbers have an LCM of 24 and a GCF of 2?

2 and 24 satisfy that request. So do 6 and 8.


What is the pair of numbers whose gcf is 1 and LCM is 36?

The pair of numbers whose GCF is 1 and LCM is 36 is 9 and 4. The numbers should be greater than their GCF and less than their LCM.


What are the math terms gcf and LCM?

GCF - Greatest Common Factor (GCF is always smaller or equal to at least one of the numbers) LCM - Least Common Multiple (LCM is always greater or equal to at least one of the numbers)


Is the GCF of 2 different numbers greater than the LCM of the numbers?

No.The gcf of two numbers is LESS THAN OR EQUAL than their lcm.The gcf of two DIFFERENT numbes is LESS THAN their lcm.


Is the gcf of two different numbers greater than the LCM of the numbers?

No. Factors go into numbers, numbers go into multiples.


How can you find the GCF of a given set of numbers given their LCM but without listing the factors of the numbers?

By finding their common prime numbers.


How do you find the other number when the one number is given with the LCM and the GCF?

The product of the original numbers is equal to the product of the GCF and LCM. Divide the product of the LCM and GCF by the one number. The answer will be the other.


2 numbers greater then one whos gcf is lesser of the two numbers and whose LCM is greater of the two numbers?

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


What do LCM and GCF have in common?

They are both found from the relationships between the members of a given set of numbers. They have kind of an inverse relationship. Since the product of the LCM and GCF of two numbers is equal to the product of the original numbers, when the GCF increases, the LCM decreases and vice versa.


How are the GCF and LCM different?

The GCF is the largest number that will divide evenly into all the members of a given set of numbers. The LCM is the smallest number that all the members of a given set will divide into. Factors go into numbers, numbers go into multiples.


What is the product of the GCF and LCM of two numbers?

The product of the GCF and LCM of a pair of numbers is equal to the product of the numbers.


How can you tell if the least common multiple of two numbers is less than or equal to the product of the numbers?

If the GCF of the two numbers is 1, the LCM will be their product. IF the GCF is greater than one, the LCM will be less than the product.


How do you change GCF into a LCM with 3 numbers?

The product of the GCF and the LCM is the same as the product of the original two numbers. Divide the product of the original numbers by the GCF. The result will be the LCM.