To find: The least common denominator of the fractions. 1) 25x+3x4 2) x2y+y3x

The least common denominator is defined as the least common multiple of the denominators of the set of fractions. Example 1: 25x+3x4 Now write each denominator as a product of prime factors, 5x=5×x 4=2×2 Now, form the product of all prime factors, L.C.D.=5×x×2×2=20x Example 2: x2y+y3x Now write each denominator as a product of prime factors, 2y=2×y 3x=3×x Now, form the product of all prime factors, L.C.D.=2×y×3×x=6xy 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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High School
Algebra
Pre-Algebra
Factors and multiples

aortiH

Answered question

2021-08-03

To find:
The least common denominator of the fractions.
1)

\frac{2}{5 x} + \frac{3 x}{4}

\frac{x}{2 y} + \frac{y}{3 x}

Answer & Explanation

Macsen Nixon

Skilled2021-08-04Added 117 answers

The least common denominator is defined as the least common multiple of the denominators of the set of fractions.
Example 1:

\frac{2}{5 x} + \frac{3 x}{4}

Now write each denominator as a product of prime factors,

5 x = 5 \times x

4 = 2 \times 2

Now, form the product of all prime factors,

L . C . D . = 5 \times x \times 2 \times 2 = 20 x

Example 2:

\frac{x}{2 y} + \frac{y}{3 x}

Now write each denominator as a product of prime factors,

2 y = 2 \times y

3 x = 3 \times x

Now, form the product of all prime factors,

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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