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.

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.