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July 22nd, 2017, 03:05 PM   #1
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Few questions about LCM and GCF in algebraic expressions , equations ?

Finding LCM involves this much steps .



Finding GCF involves this much steps too ?



?
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July 22nd, 2017, 04:21 PM   #2
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What is your question?

The algorithms given are the most efficient GENERAL algorithms. That does not mean that they are the most efficient in every case.

To turn 6x + 4 into a product of a constant and a sum, the most efficient algorithm is to find a constant that is common to 6x and 4. That is 2.

$6x + 4 = 2 * 3x + 2 * 2 = 2(3x + 2).$

Finding the least common multiple is not necessary to deal with equations involving rational functions. An alternative is to clear fractions by multiplying both sides by the product of all the denominators.

$\dfrac{7}{4x} - \dfrac{3}{x^2} = \dfrac{1}{2x^2} \implies 4x * x^2 * 2x^2 \left ( \dfrac{7}{4x} - \dfrac{3}{x^2} \right ) = 4x * x^2 * 2x^2 * \dfrac{1}{2x^2} \implies$

$7 * x^2 * 2x^2 - 3 * 4x * 2x^2 = 1 * 4x * x^2 \implies 14x^4 - 24x^3 = 4x^3 \implies$

$14x^4 = 28x^3 \implies x^4 = 2x^3 \implies \dfrac{x^4}{x^3} = \dfrac{2x^3}{x^3}\ \because \ x \ne 0.$

$\therefore x = 2.$
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July 22nd, 2017, 08:05 PM   #3
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Thanks for the reply.

About part A of that question, I am only looking for beginner level methods of finding LCMs.

About part B of that question, I think that was the method of finding common factors; is it the same as trying to find a GCF of two algebraic terms?

Last edited by skipjack; July 23rd, 2017 at 05:24 AM.
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July 23rd, 2017, 04:21 AM   #4
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Quote:
Originally Posted by awholenumber View Post
Thanks for the reply.

About part A of that question, I am only looking for beginner level methods of finding LCMs.

About part B of that question, I think that was the method of finding common factors; is it the same as trying to find a GCF of two algebraic terms?
With respect to part A, I gather you are asking whether there is a quicker method for finding a least common multiple. I answer that in two ways. First, any method for finding a LCM will turn out to be effectively equivalent to the method given. Second, the method given can be time-consuming, but, if you are willing to make your calculator do more arithmetic, you frequently do not need to find a LCM at all. A LCM was frequently a time-saver when doing arithmetic by hand, but it frequently is a time-waster when using a calculator for arithmetic.

With respect to part B, steps 1 through 3 apply only to the known numbers that are integers or can be expressed as a ratio of integers. Those steps cannot be applied to irrational numbers or unknown numbers; for those, you start at step 4.

Last edited by skipjack; July 23rd, 2017 at 05:29 AM.
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July 23rd, 2017, 05:00 AM   #5
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OK, Thanks a lot.

Last edited by skipjack; July 23rd, 2017 at 05:29 AM.
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