SOLUTION: Find the least common multiple of each pair of polynomials. 3x(x+2) and 6x(2x-3) I think the LCM is 6x but i'm not sure. Please show work so I know how you got your answer.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the least common multiple of each pair of polynomials. 3x(x+2) and 6x(2x-3) I think the LCM is 6x but i'm not sure. Please show work so I know how you got your answer.       Log On


   

Question 420174: Find the least common multiple of each pair of polynomials.
3x(x+2) and 6x(2x-3)
I think the LCM is 6x but i'm not sure.
Please show work so I know how you got your answer.
Thanks
Found 2 solutions by stanbon, dnanos:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the least common multiple of each pair of polynomials.
3x(x+2) and 6x(2x-3)
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The least common multiple must have each of the prime
factors in their highest power.
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Your Problem:
LCM = 2*3*x*(x+2)(2x-3) = 6x(2x^2+x-6) = 12x^3+6x^2-36x
This is the smallest expressing into which 3x(x+2)
and 6x(2x-3) can divide evenly.
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Cheers,
Stan H.
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Answer by dnanos(83) About Me  (Show Source):
You can put this solution on YOUR website!
You must gather all common and uncommon prime factors and form a product of all of them
using each one by the greatest exponent (if there are exponents).
So:
3x%28x%2B2%29 and 3%2A2%282x-3%29
have the LCM=3%2A2x%28x%2B2%29%282x-3%29=6x(x+2)(2x+3)