Explain how to find the LCD of two fractions.

Sherry Becker

Sherry Becker

Answered question

2021-11-17

Explain how to find the LCD of two fractions.

Answer & Explanation

James Kilian

James Kilian

Beginner2021-11-18Added 20 answers

Calculation:
To find the LCD of two fractions, first convert the denominator into prime factor.
Let the set of fraction 34 and 59.
Factors the denominator into prime factor.
4=22
9=33
Now, the product is LCM of denominator.
2233=36.
Hence, the least common denominator is 36.
user_27qwe

user_27qwe

Skilled2023-05-26Added 375 answers

Step 1: Prime Factorization
Prime factorize the denominators of the given fractions. Write each denominator as a product of prime numbers.
Let's say we have two fractions: ab and cd, where b and d are the denominators.
Step 2: List the Prime Factors
List all the prime factors obtained from the prime factorization of b and d.
For example, if the prime factorization of b is p1x1·p2x2·p3x3 and the prime factorization of d is p1y1·p2y2·p3y3, where p1,p2,p3 are prime factors, and x1,x2,x3,y1,y2,y3 are their respective exponents, then the list of prime factors would be p1,p2,p3.
Step 3: Determine the Maximum Exponent
Find the maximum exponent for each prime factor in the list obtained from Step 2. This maximum exponent will be used to construct the LCD.
Let's denote the maximum exponents as m1,m2,m3.
Step 4: Construct the LCD
The LCD is obtained by multiplying the prime factors with their corresponding maximum exponents:
LCD=p1m1·p2m2·p3m3
Step 5: Simplify the Expression
If the LCD contains multiple instances of the same prime factor, simplify the expression by removing duplicate factors. The simplified LCD is the final result.
For example, if the LCD obtained in Step 4 is q2·r3·s2·t, you can simplify it to q2·r3·s2·t.
karton

karton

Expert2023-05-26Added 613 answers

To find the least common denominator (LCD) of two fractions, you can follow these steps:
1. Start by writing the given fractions in the form of ab and cd, where a, b, c, and d are integers.
2. Determine the denominators b and d of the fractions.
3. Find the prime factors of b and d. Express b and d as the product of their prime factors. For example, if b=2·2·3 and d=2·5, then b=22·3 and d=2·5.
4. Identify all the prime factors that appear in either b or d. Include each factor the greatest number of times it appears in either b or d. In the example above, the prime factors are 2, 2, 3, and 5.
5. Multiply these prime factors together to obtain the LCD. In this case, the LCD would be 22·3·5, which can be written as 20.
By finding the LCD of the two fractions, you can then rewrite the fractions with a common denominator and perform operations such as addition or subtraction.

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