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In number theory, the product of two positive integers will equal the product of their GCF and LCM. Dividing that product by one of them will give you the other.

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โˆ™ 2015-11-10 03:50:54
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Q: Why does dividing the product by the GCF always give you the LCM?
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Why does the product of two fractions has the same value before and after dividing the numerator and denominator by the greatest common factor?

If you are dividing the numerator and the denominator by the same number (the GCF), it is the same as dividing the fraction by 1, which will leave it unchanged and create the same product.


How Have You Used GCF When Working With Fractions?

Finding the GCF of the numerator and denominator and dividing them both by it will give you the simplest form of the fraction.


What is the LCM of two numbers if their GCF is 5 and their product is 1296?

As a general principle, you can find the LCM of two numbers by dividing their product by their GCF. This one won't work. The product of any two numbers with 5 as a common factor would have to end in 5 or 0.


What is the relationship of the product to the product of gcf and LCM?

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


What is the product of the GCF and LCM of 4 and 6?

2 x 12 = 24, but there's an easier way if you remember that the product of the GCF and LCM of a pair of numbers will always be equal to the product of the two numbers.


How do you use a gcf?

i use a GCF to simplify a fraction by dividing it into both the numerator and the denominator.


How do you compare the product of the GCF and the LCM?

The product of the GCF and LCM of two numbers is the same as the product of the numbers.


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 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.


How can the GCF help you with fractions?

Finding the GCF of the numerator and the denominator and dividing them both by it is the way to simplify a fraction.


Which product is the gcf of 30 and 32?

The GCF is 2.


Is the GCF of any two numbers is always odd?

The GCF of any two odd numbers is always odd. The GCF of any two even numbers is always even. The GCF of an odd and an even number is always odd.


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.


How do you find the LCM using GCF?

The GCF of two numbers multiplied by their LCM will equal the product of the original numbers. If you know the GCF, divide it into the product of the two. The result will be the LCM. If the GCF of two numbers is 1, the LCM is their product.


What is the least common multiple of 49 and 63?

The LCM of 49 and 63 is 441. You can find the LCM of a set of numbers by finding their product, and dividing it by their GCF. The product of 49 and 63 is 3087. The GCF of 49 and 63 is 7. (49 = 7*7 and 63 = 7*9, so their GCF is 7.) 3087 / 7 = 441.


What is the least common multiple of 35 and 85?

The LCM of 35 and 85 is 595 You can find the LCM by dividing the product of the pair of integers by their GCF. The product of 35 and 85 is 2975 The GCF of 35 and 85 is 5 (35 = 5*7 and 85 = 5* 17, so their GCF is 5.) 2975 / 5 = 595


Is there a relationship between GCF and LCM?

The product of the GCF and LCM of two numbers is the same as the product of the two numbers.


Could you divide the product by the GCF to find the LCM?

Yes, you could divide the product by the GCF to find the LCM


How do you make up a problem to find the lcm of two numbers of one to find gcf of two numbers?

You can find the GCF of two numbers by dividing their product by their LCM. The LCM of 30 and 42 is 210. What is their GCF? 30 x 42 = 1260 divided by 210 = 6 The GCF of 30 and 42 is 6.


How do you check lcm answer?

One way to check: The product of the original two numbers is equal to the product of their GCF and LCM. If you divide that product by their GCF, you will get the LCM.


How do you find GCF knowing LCM?

The LCM of two numbers multiplied by their GCF will equal the product of the original numbers. If you know the LCM, divide it into the product. The result will be the GCF.


What is the quickest way to find the GCF and LCM?

Dividing them by prime numbers


How can you use the Euclidean Algorithm to find the GCF of three numbers?

By dividing


What is the GCF and LCM of 27 and 16?

The GCF is 1. The LCM is their product.


What is the LCM of 2 number that have on GCF then 1 give an example?

The LCM is their product. The GCF of 4 and 9 is 1. The LCM of 4 and 9 is 36.

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