What Is The LCD Of 2x^2, 6y, and 3xy?Having A Hard Time Figuring This Out. Please Help & Thanks!

Expert Answers
embizze eNotes educator| Certified Educator

Find the LCD of `2x^2,6y,3xy` :

One method is to fully factor every term:




The LCD includes every factor that appears to the highest degree that it appears.

We have a 2, a 3, an x whose highest degree is `x^2` , and a y.

Then the LCD is `2*3*x^2*y=6x^2y`

Note that `6x^2y=3y(2x^2),6x^2y=x^2(6y),6x^2y=2x(3xy)`


jgr12889 | Student

One method to solve for the LCD is to get all variables to the highest existing degree and all numbers to the LCM.

First, I would list the numbers 2, 3, 6.  By looking at this list I can determine that my LCM is 6, since all numbers can be multiplied by another number to get to 6.  Therefore, 6 is the numerical part of my LCD.

Next, look at the 'x' terms; x^2, x^0, x^1.  I included the exponents for all the elements so it is easier to see what the highest is.  Remember that x^0=1, so the term 6y still technically has an 'x' variable in it.  Anyway, when looking at the list, clearly x^2 is the highest power, and thus part of our LCD.  All other numbers are multiples if their value is less than 2, because when multiplying exponents, we add the values of the powers.

We take the same approach for 'y' as we did for 'x'.  So, we get y^0, y^1, y^1.  This shows that the highest exponent is y^1 and is part of our LCD.

Now, put all the terms we found to be part of our LCD together and get our final answer of; 6 x^2 y^1.

P.S. The equation writer was not working at the time of this response, I hope all the math still makes sense.  Sorry for the inconvenience!