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July 22nd, 2017, 03:05 PM  #1 
Member Joined: Jun 2017 From: India Posts: 65 Thanks: 3  Few questions about LCM and GCF in algebraic expressions , equations ?
Finding LCM involves this much steps . Finding GCF involves this much steps too ? ? 
July 22nd, 2017, 04:21 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,047 Thanks: 430 
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. $\dfrac{7}{4x}  \dfrac{3}{x^2} = \dfrac{1}{2x^2} \implies 4x * x^2 * 2x^2 \left ( \dfrac{7}{4x}  \dfrac{3}{x^2} \right ) = 4x * x^2 * 2x^2 * \dfrac{1}{2x^2} \implies$ $7 * x^2 * 2x^2  3 * 4x * 2x^2 = 1 * 4x * x^2 \implies 14x^4  24x^3 = 4x^3 \implies$ $14x^4 = 28x^3 \implies x^4 = 2x^3 \implies \dfrac{x^4}{x^3} = \dfrac{2x^3}{x^3}\ \because \ x \ne 0.$ $\therefore x = 2.$ 
July 22nd, 2017, 08:05 PM  #3 
Member Joined: Jun 2017 From: India Posts: 65 Thanks: 3 
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. 
July 23rd, 2017, 04:21 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 1,047 Thanks: 430  Quote:
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.  
July 23rd, 2017, 05:00 AM  #5 
Member Joined: Jun 2017 From: India Posts: 65 Thanks: 3 
OK, Thanks a lot.
Last edited by skipjack; July 23rd, 2017 at 05:29 AM. 

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algebraic, equations, expressions, gcf, lcm, questions 
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