Question

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

Factors and multiples
To find:
The least common denominator of the fractions.
1) $$\displaystyle{25}{x}+{3}{x}{4}$$
2) $$\displaystyle{x}{2}{y}+{y}{3}{x}$$

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.