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anonymous

  • one year ago

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

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  1. mathstudent55
    • one year ago
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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.

  2. anonymous
    • one year ago
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    then what would the LCD be of the first expression?

  3. anonymous
    • one year ago
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    @mathstudent55

  4. mathstudent55
    • one year ago
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    To find the LCD, use common and not common factors with the largest exponent. I'll explain what that means.

  5. mathstudent55
    • one year ago
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    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.

  6. mathstudent55
    • one year ago
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    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

  7. anonymous
    • one year ago
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    Thanks so much!

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