Question 714885: find the least common multiple
x^+8x, x^2-8x
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! I assume that the first expression is x^2+8x.
To find a least common multiple you need to know what the factors of the two expressions are. And I find that it can be helpful to factor in a certain way:
x^2+8x = 1 * x * (x+8)
x^2-8x = 1 * x * (x-8)
LCM = 1 * x * (x+8) * (x-8) = x * (x^2-64) = x^3-64x
Note how I used spacing so each column has the same factor in it. Both expressions have a factor of x. The other factors are different so they go in different columns. Once you have arranged the factors this way, the LCM is simply of a factor from each column.
P.S. This technique can also be used to find greatest common factors (GCF's). But instead of using factors from every column, a GCF is the product of just the "full" columns, just the columns that have an entry in every row. In this case, the GCF would be 1 * x or just x.
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