Can a variable be a least common denominator if it is the only common denominator?

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Can a variable be a least common denominator if it is the only common denominator?

Mathematics
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\(\dfrac{5y}{2x^2} + \dfrac{3z}{3x}\) The only common factor of the denominators is x. x is not the LCD. \(\dfrac{y}{x} - \dfrac{z}{x} \) x is the the only common factor of the two denominators, and x is the LCD.
then what would the LCD be of the first expression?

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To find the LCD, use common and not common factors with the largest exponent. I'll explain what that means.
What is the LCD of 180 and 108? First, we find the prime factors of each number. \(180 = 2^2 \times 3^2 \times 5\) \(108 = 2^2 \times 3^3\) As you can see, both 180 and 108 have 2 and 3 as factors. 180 also has 5 as a factor, but 108 does not have 5 as a factor. To find the LCD of 180 and 108, we follow the rule. We need common and not common factors with the largest exponent. We have common factor 2 appearing as 2^2, and 2^2. Pick 2^2 (2 is the only exponent of factor 2, so pick it). Then we have common factor 3^2 and 3^3. Pick 3^3 (the larger of the two exponents) Finally, there is not common exponent 5, which only 180 has. Pick it also. LCD = 2^2 * 3^3 * 5 = 4 * 27 * 5 = 540 The LCD of 180 and 108 is 540.
Now let's look at my example with variables above. What is the LCD of 2x^2 and 3x? 2x^2 = 2 * x^2 3x = 3 * x LCD = 2 * 3 * x^2 = 6x^2
Thanks so much!

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