Solved on Jan 08, 2024

Find the least common denominator (LCD) of the set of fractions $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$ .

STEP 1

Assumptions
1. We are given a set of fractions: $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$ .
2. We need to find the least common denominator (LCD) for these fractions.
3. The LCD is the smallest number that each of the denominators can divide into without leaving a remainder.

STEP 2

List the denominators of the given fractions.
$Denominators: 2, 3, 4$

STEP 3

Find the prime factors of each denominator.
$2 = 2$ $3 = 3$ $4 = 2 \times 2$

STEP 4

Identify the unique prime factors from the list of prime factors of each denominator.
$Unique\, prime\, factors: 2, 3$

STEP 5

For each unique prime factor, take the highest power of that factor that appears in any of the denominators.
$For\, 2: The\, highest\, power\, is\, 2^2\, (from\, 4)$ $For\, 3: The\, highest\, power\, is\, 3^1\, (from\, 3)$

STEP 6

Multiply these highest powers together to find the LCD.
$LCD = 2^2 \times 3^1$

STEP 7

Calculate the LCD.
$LCD = 4 \times 3 = 12$
The least common denominator (LCD) of the set of fractions $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$ is 12.

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Find the least common denominator (LCD) of the set of fractions $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$ .

STEP 1

Assumptions
1. We are given a set of fractions: $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$ .
2. We need to find the least common denominator (LCD) for these fractions.
3. The LCD is the smallest number that each of the denominators can divide into without leaving a remainder.

STEP 2

List the denominators of the given fractions.
$Denominators: 2, 3, 4$

STEP 3

Find the prime factors of each denominator.
$2 = 2$ $3 = 3$ $4 = 2 \times 2$

STEP 4

Identify the unique prime factors from the list of prime factors of each denominator.
$Unique\, prime\, factors: 2, 3$

STEP 5

For each unique prime factor, take the highest power of that factor that appears in any of the denominators.
$For\, 2: The\, highest\, power\, is\, 2^2\, (from\, 4)$ $For\, 3: The\, highest\, power\, is\, 3^1\, (from\, 3)$

STEP 6

Multiply these highest powers together to find the LCD.
$LCD = 2^2 \times 3^1$

STEP 7

Calculate the LCD.
$LCD = 4 \times 3 = 12$
The least common denominator (LCD) of the set of fractions $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$ is 12.

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Find the least common denominator (LCD) of the set of fractions 12,23,34\frac{1}{2}, \frac{2}{3}, \frac{3}{4}21​,32​,43​.

STEP 1

Assumptions1. We are given a set of fractions: 12,23,34\frac{1}{2}, \frac{2}{3}, \frac{3}{4}21​,32​,43​.2. We need to find the least common denominator (LCD) for these fractions.3. The LCD is the smallest number that each of the denominators can divide into without leaving a remainder.

STEP 2

List the denominators of the given fractions.Denominators:2,3,4Denominators: 2, 3, 4Denominators:2,3,4

STEP 3

Find the prime factors of each denominator.2=22 = 22=2 3=33 = 33=3 4=2×24 = 2 \times 24=2×2

STEP 4

Identify the unique prime factors from the list of prime factors of each denominator.Unique prime factors:2,3Unique\, prime\, factors: 2, 3Uniqueprimefactors:2,3

STEP 5

STEP 6

Multiply these highest powers together to find the LCD.LCD=22×31LCD = 2^2 \times 3^1LCD=22×31

STEP 7

Calculate the LCD.LCD=4×3=12LCD = 4 \times 3 = 12LCD=4×3=12The least common denominator (LCD) of the set of fractions 12,23,34\frac{1}{2}, \frac{2}{3}, \frac{3}{4}21​,32​,43​ is 12.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the least common denominator (LCD) of the set of fractions $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$ .

Assumptions
1. We are given a set of fractions: $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$ .
2. We need to find the least common denominator (LCD) for these fractions.
3. The LCD is the smallest number that each of the denominators can divide into without leaving a remainder.

List the denominators of the given fractions.
$Denominators: 2, 3, 4$

Find the prime factors of each denominator.
$2 = 2$ $3 = 3$ $4 = 2 \times 2$

Identify the unique prime factors from the list of prime factors of each denominator.
$Unique\, prime\, factors: 2, 3$

Multiply these highest powers together to find the LCD.
$LCD = 2^2 \times 3^1$

Calculate the LCD.
$LCD = 4 \times 3 = 12$
The least common denominator (LCD) of the set of fractions $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$ is 12.