Explain how to find the LCD of two fractions.

Question

James Kilian · Accepted Answer

Calculation:
To find the LCD of two fractions, first convert the denominator into prime factor.
Let the set of fraction

\frac{3}{4} and \frac{5}{9}

.
Factors the denominator into prime factor.

4 = 2 \cdot 2

9 = 3 \cdot 3

Now, the product is LCM of denominator.

2 \cdot 2 \cdot 3 \cdot 3 = 36

.
Hence, the least common denominator is 36.

user_27qwe · Accepted Answer

Step 1: Prime FactorizationPrime factorize the denominators of the given fractions. Write each denominator as a product of prime numbers.Let&#039;s say we have two fractions: ab and cd, where b and d are the denominators.Step 2: List the Prime FactorsList 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 ExponentFind 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&#039;s denote the maximum exponents as m1,m2,m3.Step 4: Construct the LCDThe LCD is obtained by multiplying the prime factors with their corresponding maximum exponents:LCD=p1m1·p2m2·p3m3Step 5: Simplify the ExpressionIf 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 · Accepted Answer

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

\frac{a}{b}

and

\frac{c}{d}

, 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 \cdot 2 \cdot 3

and

d = 2 \cdot 5

, then

b = 2^{2} \cdot 3

and

d = 2 \cdot 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

2^{2} \cdot 3 \cdot 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.

Explain how to find the LCD of two fractions.

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