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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.

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Algebra

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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Q: Why is the least common multiple of two numbers their product divided by their greatest common factor?
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Related questions

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.


Is it true that the Least Common Multiple of two numbers is equal to their product divided by their Greatest Common Factor?

Yes.


If you know that two numbers are relatively prime can you predict what the least common multiple will be?

The least common multiple of two numbers is the product of those two numbers, divided by the greatest common factor of those two numbers. Two numbers that are relatively prime have a greatest common factor of 1. So, when the two numbers are relatively prime, the least common multiple is the product of both numbers divided by 1. So, when two numbers are relatively prime, the least common multiple is the product of the two numbers.this is wron


What is the least common multiple of 28 and 48?

The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 28 and 48 is 4. Therefore, the least common multiple is 28 x 48 ÷ 4 = 336.


What is the least common multiple of 15 and 32?

The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 15 and 32 is 1, so the least common multiple is 15 x 32 ÷ 1 = 480.


What is the least common multiple of 7 and 159?

The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 7 and 159 is 1, so the least common multiple is 7 x 159 ÷ 1 = 1113.


What is the least common multiple of 56 and 64?

The least common multiple is the product of the two numbers divided by their greatest common factor. Their greatest common factor is 8, so the least common multiple is 56 x 64 ÷ 8 = 448.


What is the least common multiple of 2 and 3?

The least common multiple of 2 and 3 is: 6The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. 2 and 3 are both prime, so their greatest common factor is 1.6


What is the greatest common multiple of two prime numbers?

The greatest common multiple is an infinite amount and not very practical for problem solving. The least common multiple of two prime numbers is their product.


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.


What is the relationship between the product of two numbers and the product of the least common multiple and greatest common factor of those two numbers?

They are equivalent.


what is the lowest common multiple of 72 and 42?

The Least Common Multiple of two numbers is equal to their product divided by their greatest common factor.The greatest common factor of 72 and 42 is 6, so their Least Common Multiple is 72 * 42 / 6 = 504.


What is the least common multiple of 44 and 60?

The least common multiple is the product of the two numbers divided by their greatest common factor. The greatest common factor of 44 and 60 is 4, so the least common multiple is 44 x 60 ÷ 4 = 660.


What is the least common multiple of 14 and 70?

Since 70 is a multiple of 14, it is the least common multiple. Or, you can determine it as you would any pair of numbers. The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 14 and 70 is 14. Therefore, the least common multiple 14 x 70 ÷ 14 = 70.


How the least common multiple of two numbers differs from the greatest common factor of the numbers?

The greatest common factor, or GCF, is the largest positive integer that will divide evenly with no remainder into all the members of a given set of numbers. The least common multiple, or LCM, is the smallest positive integer that all the members of a given set of numbers will divide into evenly with no remainder. Factors go into numbers, numbers go into multiples. Since the product of the GCF and LCM of two numbers equals the product of the two numbers themselves, the GCF of two numbers will equal the product of the numbers divided by the LCM and the LCM of two numbers will equal their product divided by their GCF.


What is the least common multiple of two prime numbers?

The LCM of prime numbers is simply their product (a x b, or x*y). The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of two prime numbers is 1. Therefore, the least common multiple of two prime numbers is the two numbers multiplied together, since dividing by 1 will not change the answer. The same applies to "relatively prime" numbers such as 10 and 21, where the GCF is also 1.


What is the least common multiple of 14 and 63?

The LCM of 14 and 63 is 126. The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 14 and 63 is 7, so the least common multiple is 14 x 63 ÷ 7 = 126.


What is the least common multiple of 5 and 23?

The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 5 and 23 is 1. (See related question "What is the greatest common factor of 5 and 23?" for this calculation.) So, the least common multiple is 5 x 23 ÷ 1 = 115.


If the greatest common factor of two whole numbers is 1 what is the least common multiple of the numbers?

The LCM of the two numbers will be their product.


What is the least common multiple of 2 coprime numbers?

The least common multiple of two numbers is the product of those two numbers divided by their greatest common factor. It the two numbers are coprime (or relatively prime), their greatest common factor is 1. Therefore, their least common multiple is a x b ÷ GCF (of a and b) = a x b ÷ 1 = a x b. The least common multiple of two coprime numbers is the numbers multiplied together.


What is the product of the greatest common factor and least common multiple of 20 and 72?

The same as the product of the original numbers, 1440.


What is the least common multiple of 16 and 26?

The LCM of 16 and 26 is 208. The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 16 and 26 is 2. Therefore, the least common multiple is 16 x 26 ÷ 2 = 208.


What is the least common multiple of 15 and 39?

The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 15 and 39 is 3. Therefore, the least common multiple of 15 and 39 is 15 x 39 ÷ 3 = 195.


How are least common multiple and greatest common factor related?

The product of the GCF and the LCM is equal to the product of the original two numbers.


What is the least common multiple of 20 and 52?

The LCM of 20 and 52 is 260. The least common multiple is the product of the two numbers divided by their greatest common factor. The greatest common factor of 20 and 52 is 4, so their least common multiple is 20 x 52 ÷ 4 = 260.