Q: Why does dividing the product by the GCF always give you the LCM?

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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.

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

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.

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

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.

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

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

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

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

The GCF is 2.

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.

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.

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.

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.

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

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

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

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.

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.

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.

Dividing them by prime numbers

By dividing

The GCF is 1. The LCM is their product.

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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