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Which of the following is the least common denominator for the expression below?
  • a)
    b x c
  • b)
    α x b x c
  • c)
    α2 x b x c
  • d)
    α2 x b2 x c2
  • e)
    α2 x b4 x c5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which of the following is the least common denominator for the express...
The correct answer is d. The least common denominator (LCD) is actually the least common multiple of the three denominators. To find the LCD, first find the greatest common factor of the denominators. In this case, each denominator contains either α, b, or both b and c, so those are the factors that they have in common. The values that remain in the three denominators represent what they don’t have in common, and are the least common multiples of each denominator. To find the least common multiple, otherwise known as the least common denominator (LCD), simply multiply the least common multiples of each denominator together, to get α2 × α2 × c2.
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Current high levels of fossil fuel use, including coal-burning power plants and gasoline-powered automobiles, have helped contribute to the high concentrations of sulfur trioxide, SO3, found in the atmosphere. When sulfur trioxide and water interact, they can undergo the following chemical reaction to produce sulfuric acid, which is the main contributor to acid rain worldwide:SO3+ H2O H2SO4Acid rain showers are particularly common near coal-burning power plants and large cities. These showers are responsible for significant economic damage to sidewalks, roads, and buildings. Scientists interested in studying the effects of acid rain often use basic substances like calcium carbonate, the main component of limestone buildings, and expose them to varying volumes of acid rain to determine what volume of acid rain is necessary to begin to erode a building. A sample graph of one scientist’s experiment is replicated below:Measuring acid and base levels is commonly done with a scale called pH, which uses the concentration of hydrogen ions to determine the acidity. Hydrogen ions are in a balance with hydroxide ions to give a scale with a range from 0 to 14. Values equal to or between 0 and 6.9 represent the acidic range where hydrogen ions predominate and values equal to or ranging from 7.1 and 14 represent the basic range where hydroxide ions predominate. Thus, the more hydrogen ions present, the more acidic the solution.Scientists can tell when a titration (pH) experiment passes a certain pH using compounds called indicators. Indicators are usually colorless at pH levels below that of their specified color change. A table of indicators used by the above scientists and the pH at which they change colors is presented below.Q.The relationship between pH and volume of acid added can best be described as which of the following?

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Current high levels of fossil fuel use, including coal-burning power plants and gasoline-powered automobiles, have helped contribute to the high concentrations of sulfur trioxide, SO3, found in the atmosphere. When sulfur trioxide and water interact, they can undergo the following chemical reaction to produce sulfuric acid, which is the main contributor to acid rain worldwide:SO3+ H2O H2SO4Acid rain showers are particularly common near coal-burning power plants and large cities. These showers are responsible for significant economic damage to sidewalks, roads, and buildings. Scientists interested in studying the effects of acid rain often use basic substances like calcium carbonate, the main component of limestone buildings, and expose them to varying volumes of acid rain to determine what volume of acid rain is necessary to begin to erode a building. A sample graph of one scientist’s experiment is replicated below:Measuring acid and base levels is commonly done with a scale called pH, which uses the concentration of hydrogen ions to determine the acidity. Hydrogen ions are in a balance with hydroxide ions to give a scale with a range from 0 to 14. Values equal to or between 0 and 6.9 represent the acidic range where hydrogen ions predominate and values equal to or ranging from 7.1 and 14 represent the basic range where hydroxide ions predominate. Thus, the more hydrogen ions present, the more acidic the solution.Scientists can tell when a titration (pH) experiment passes a certain pH using compounds called indicators. Indicators are usually colorless at pH levels below that of their specified color change. A table of indicators used by the above scientists and the pH at which they change colors is presented below.Q. What is the pH of a solution containing calcium carbonate and sulfuric acid when 20 mL of sulfuric acid have been added?

Current high levels of fossil fuel use, including coal-burning power plants and gasoline-powered automobiles, have helped contribute to the high concentrations of sulfur trioxide, SO3, found in the atmosphere. When sulfur trioxide and water interact, they can undergo the following chemical reaction to produce sulfuric acid, which is the main contributor to acid rain worldwide:SO3+ H2O H2SO4Acid rain showers are particularly common near coal-burning power plants and large cities. These showers are responsible for significant economic damage to sidewalks, roads, and buildings. Scientists interested in studying the effects of acid rain often use basic substances like calcium carbonate, the main component of limestone buildings, and expose them to varying volumes of acid rain to determine what volume of acid rain is necessary to begin to erode a building. A sample graph of one scientist’s experiment is replicated below:Measuring acid and base levels is commonly done with a scale called pH, which uses the concentration of hydrogen ions to determine the acidity. Hydrogen ions are in a balance with hydroxide ions to give a scale with a range from 0 to 14. Values equal to or between 0 and 6.9 represent the acidic range where hydrogen ions predominate and values equal to or ranging from 7.1 and 14 represent the basic range where hydroxide ions predominate. Thus, the more hydrogen ions present, the more acidic the solution.Scientists can tell when a titration (pH) experiment passes a certain pH using compounds called indicators. Indicators are usually colorless at pH levels below that of their specified color change. A table of indicators used by the above scientists and the pH at which they change colors is presented below.Q. What is the pH of a solution containing calcium carbonate and sulfuric acid when 29 mL of sulfuric acid have been added?

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Which of the following is the least common denominator for the expression below?a)b x cb)α x b x cc)α2 x b x cd)α2 x b2 x c2e)α2 x b4 x c5Correct answer is option 'D'. Can you explain this answer?
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