Question

To find: The least common denominator of the fractions. 25x+3x4 x2y+y3x

Factors and multiples
ANSWERED
asked 2021-08-08
To find:
The least common denominator of the fractions.
1) \(\displaystyle{25}{x}+{3}{x}{4}\)
2) \(\displaystyle{x}{2}{y}+{y}{3}{x}\)

Answers (1)

2021-08-09
The least common denominator is defined as the least common multiple of the denominators of the set of fractions.
Example 1:
\(\displaystyle{25}{x}+{3}{x}{4}\)
Now write each denominator as a product of prime factors,
\(\displaystyle{5}{x}={5}\times{x}{4}={2}\times{2}\)
Now, form the product of all prime factors,
\(\displaystyle{L}.{C}.{D}.={5}\times{x}\times{2}\times{2}={20}{x}\)
Example 2:
\(\displaystyle{x}{2}{y}+{y}{3}{x}\)
Now write each denominator as a product of prime factors,
\(\displaystyle{2}{y}={2}\times{y}{3}{x}={3}\times{x}\)
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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