Solved on Feb 29, 2024

Find the least common denominator (LCD) to solve the linear equation $\frac{1}{5}x + \frac{1}{2}x = \frac{1}{3}$ .

STEP 1

Assumptions
1. The given equation is $\frac{1}{5} x + \frac{1}{2} x = \frac{1}{3}$ .
2. We need to find the least common denominator (LCD) of the fractional coefficients to eliminate the fractions.

STEP 2

Identify the denominators of the fractional coefficients in the equation.
The denominators are 5, 2, and 3 for the fractions $\frac{1}{5}$ , $\frac{1}{2}$ , and $\frac{1}{3}$ respectively.

STEP 3

Find the least common multiple (LCM) of the denominators, which will be the least common denominator (LCD) for the equation.
The denominators are 5, 2, and 3.

STEP 4

List the prime factors of each denominator.
- Prime factors of 5: 5 - Prime factors of 2: 2 - Prime factors of 3: 3

STEP 5

For each prime factor, take the highest power that appears in any of the denominators.
- For the prime factor 5: The highest power is $5^1$ . - For the prime factor 2: The highest power is $2^1$ . - For the prime factor 3: The highest power is $3^1$ .

STEP 6

Multiply these highest powers together to find the LCD.
$LCD = 5^1 \times 2^1 \times 3^1$

STEP 7

Calculate the LCD.
$LCD = 5 \times 2 \times 3$

STEP 8

Multiply the numbers to find the LCD.
$LCD = 5 \times 2 \times 3 = 30$
The least common denominator (LCD) is 30.

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Find the least common denominator (LCD) to solve the linear equation $\frac{1}{5}x + \frac{1}{2}x = \frac{1}{3}$ .

STEP 1

Assumptions
1. The given equation is $\frac{1}{5} x + \frac{1}{2} x = \frac{1}{3}$ .
2. We need to find the least common denominator (LCD) of the fractional coefficients to eliminate the fractions.

STEP 2

Identify the denominators of the fractional coefficients in the equation.
The denominators are 5, 2, and 3 for the fractions $\frac{1}{5}$ , $\frac{1}{2}$ , and $\frac{1}{3}$ respectively.

STEP 3

Find the least common multiple (LCM) of the denominators, which will be the least common denominator (LCD) for the equation.
The denominators are 5, 2, and 3.

STEP 4

List the prime factors of each denominator.
- Prime factors of 5: 5 - Prime factors of 2: 2 - Prime factors of 3: 3

STEP 5

For each prime factor, take the highest power that appears in any of the denominators.
- For the prime factor 5: The highest power is $5^1$ . - For the prime factor 2: The highest power is $2^1$ . - For the prime factor 3: The highest power is $3^1$ .

STEP 6

Multiply these highest powers together to find the LCD.
$LCD = 5^1 \times 2^1 \times 3^1$

STEP 7

Calculate the LCD.
$LCD = 5 \times 2 \times 3$

STEP 8

Multiply the numbers to find the LCD.
$LCD = 5 \times 2 \times 3 = 30$
The least common denominator (LCD) is 30.

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Find the least common denominator (LCD) to solve the linear equation 15x+12x=13\frac{1}{5}x + \frac{1}{2}x = \frac{1}{3}51​x+21​x=31​.

STEP 1

Assumptions1. The given equation is 15x+12x=13\frac{1}{5} x + \frac{1}{2} x = \frac{1}{3}51​x+21​x=31​.2. We need to find the least common denominator (LCD) of the fractional coefficients to eliminate the fractions.

STEP 2

Identify the denominators of the fractional coefficients in the equation.The denominators are 5, 2, and 3 for the fractions 15\frac{1}{5}51​, 12\frac{1}{2}21​, and 13\frac{1}{3}31​ respectively.

STEP 3

Find the least common multiple (LCM) of the denominators, which will be the least common denominator (LCD) for the equation.The denominators are 5, 2, and 3.

STEP 4

List the prime factors of each denominator.- Prime factors of 5: 5 - Prime factors of 2: 2 - Prime factors of 3: 3

STEP 5

For each prime factor, take the highest power that appears in any of the denominators.- For the prime factor 5: The highest power is 515^151. - For the prime factor 2: The highest power is 212^121. - For the prime factor 3: The highest power is 313^131.

STEP 6

Multiply these highest powers together to find the LCD.LCD=51×21×31LCD = 5^1 \times 2^1 \times 3^1LCD=51×21×31

STEP 7

Calculate the LCD.LCD=5×2×3LCD = 5 \times 2 \times 3LCD=5×2×3

STEP 8

Multiply the numbers to find the LCD.LCD=5×2×3=30LCD = 5 \times 2 \times 3 = 30LCD=5×2×3=30The least common denominator (LCD) is 30.

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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) to solve the linear equation $\frac{1}{5}x + \frac{1}{2}x = \frac{1}{3}$ .

Assumptions
1. The given equation is $\frac{1}{5} x + \frac{1}{2} x = \frac{1}{3}$ .
2. We need to find the least common denominator (LCD) of the fractional coefficients to eliminate the fractions.

Identify the denominators of the fractional coefficients in the equation.
The denominators are 5, 2, and 3 for the fractions $\frac{1}{5}$ , $\frac{1}{2}$ , and $\frac{1}{3}$ respectively.

Find the least common multiple (LCM) of the denominators, which will be the least common denominator (LCD) for the equation.
The denominators are 5, 2, and 3.

List the prime factors of each denominator.
- Prime factors of 5: 5 - Prime factors of 2: 2 - Prime factors of 3: 3

For each prime factor, take the highest power that appears in any of the denominators.
- For the prime factor 5: The highest power is $5^1$ . - For the prime factor 2: The highest power is $2^1$ . - For the prime factor 3: The highest power is $3^1$ .

Multiply these highest powers together to find the LCD.
$LCD = 5^1 \times 2^1 \times 3^1$

Calculate the LCD.
$LCD = 5 \times 2 \times 3$

Multiply the numbers to find the LCD.
$LCD = 5 \times 2 \times 3 = 30$
The least common denominator (LCD) is 30.