Question

To find: The least common denominator of the fractions. \frac{2}{5x} + \frac{3x}{4} \frac{x}{2y} + \frac{y}{3x}

Factors and multiples
ANSWERED
asked 2021-08-03
To find:
The least common denominator of the fractions.
1) \(\displaystyle{\frac{{{2}}}{{{5}{x}}}}+{\frac{{{3}{x}}}{{{4}}}}\)
2) \(\displaystyle{\frac{{{x}}}{{{2}{y}}}}+{\frac{{{y}}}{{{3}{x}}}}\)

Answers (1)

2021-08-04
The least common denominator is defined as the least common multiple of the denominators of the set of fractions.
Example 1:
\(\displaystyle{\frac{{{2}}}{{{5}{x}}}}+{\frac{{{3}{x}}}{{{4}}}}\)
Now write each denominator as a product of prime factors,
\(\displaystyle{5}{x}={5}\times{x}\)
\(\displaystyle{4}={2}\times{2}\)
Now, form the product of all prime factors,
\(\displaystyle{L}.{C}.{D}.={5}\times{x}\times{2}\times{2}={20}{x}\)
Example 2:
\(\displaystyle{\frac{{{x}}}{{{2}{y}}}}+{\frac{{{y}}}{{{3}{x}}}}\)
Now write each denominator as a product of prime factors,
\(\displaystyle{2}{y}={2}\times{y}\)
\(\displaystyle{3}{x}={3}\times{x}\)
Now, form the product of all prime factors,
\(\displaystyle{L}.{C}.{D}.={2}\times{y}\times{3}\times{x}={6}{x}{y}\)
The Final Statement:
The least common denominator is defined as the least common multiple of the denominators of the set of fractions.
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