Solved on Jan 03, 2024

Find the least common denominator (LCD) of 25, 50, and $75$ .

STEP 1

Assumptions
1. We need to find the least common denominator (LCD) for the numbers 25, 50, and 75.
2. The LCD is the smallest number that all the given numbers can divide into without leaving a remainder.

STEP 2

First, we will list the prime factors of each number to find the LCD.
$25 = 5^2$ $50 = 2 \times 5^2$ $75 = 3 \times 5^2$

STEP 3

Identify the unique prime factors from all the numbers. In this case, the unique prime factors are 2, 3, and 5.

STEP 4

For each unique prime factor, choose the highest power that appears in the factorization of any of the numbers.
For 2: The highest power is $2^1$ (from 50). For 3: The highest power is $3^1$ (from 75). For 5: The highest power is $5^2$ (which appears in all three numbers).

STEP 5

Multiply these highest powers of all the unique prime factors to find the LCD.
$LCD = 2^1 \times 3^1 \times 5^2$

STEP 6

Calculate the LCD by multiplying the numbers.
$LCD = 2 \times 3 \times 25$

STEP 7

Perform the multiplication to find the LCD.
$LCD = 2 \times 3 \times 25 = 6 \times 25 = 150$
The least common denominator (LCD) of 25, 50, and 75 is 150.

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Find the least common denominator (LCD) of 25, 50, and $75$ .

STEP 1

Assumptions
1. We need to find the least common denominator (LCD) for the numbers 25, 50, and 75.
2. The LCD is the smallest number that all the given numbers can divide into without leaving a remainder.

STEP 2

First, we will list the prime factors of each number to find the LCD.
$25 = 5^2$ $50 = 2 \times 5^2$ $75 = 3 \times 5^2$

STEP 3

Identify the unique prime factors from all the numbers. In this case, the unique prime factors are 2, 3, and 5.

STEP 4

For each unique prime factor, choose the highest power that appears in the factorization of any of the numbers.
For 2: The highest power is $2^1$ (from 50). For 3: The highest power is $3^1$ (from 75). For 5: The highest power is $5^2$ (which appears in all three numbers).

STEP 5

Multiply these highest powers of all the unique prime factors to find the LCD.
$LCD = 2^1 \times 3^1 \times 5^2$

STEP 6

Calculate the LCD by multiplying the numbers.
$LCD = 2 \times 3 \times 25$

STEP 7

Perform the multiplication to find the LCD.
$LCD = 2 \times 3 \times 25 = 6 \times 25 = 150$
The least common denominator (LCD) of 25, 50, and 75 is 150.

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Find the least common denominator (LCD) of 25, 50, and 757575.

STEP 1

Assumptions1. We need to find the least common denominator (LCD) for the numbers 25, 50, and 75.2. The LCD is the smallest number that all the given numbers can divide into without leaving a remainder.

STEP 2

First, we will list the prime factors of each number to find the LCD.25=5225 = 5^225=52 50=2×5250 = 2 \times 5^250=2×52 75=3×5275 = 3 \times 5^275=3×52

STEP 3

Identify the unique prime factors from all the numbers. In this case, the unique prime factors are 2, 3, and 5.

STEP 4

For each unique prime factor, choose the highest power that appears in the factorization of any of the numbers.For 2: The highest power is 212^121 (from 50). For 3: The highest power is 313^131 (from 75). For 5: The highest power is 525^252 (which appears in all three numbers).

STEP 5

Multiply these highest powers of all the unique prime factors to find the LCD.LCD=21×31×52LCD = 2^1 \times 3^1 \times 5^2LCD=21×31×52

STEP 6

Calculate the LCD by multiplying the numbers.LCD=2×3×25LCD = 2 \times 3 \times 25LCD=2×3×25

STEP 7

Perform the multiplication to find the LCD.LCD=2×3×25=6×25=150LCD = 2 \times 3 \times 25 = 6 \times 25 = 150LCD=2×3×25=6×25=150The least common denominator (LCD) of 25, 50, and 75 is 150.

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 25, 50, and $75$ .

Assumptions
1. We need to find the least common denominator (LCD) for the numbers 25, 50, and 75.
2. The LCD is the smallest number that all the given numbers can divide into without leaving a remainder.

First, we will list the prime factors of each number to find the LCD.
$25 = 5^2$ $50 = 2 \times 5^2$ $75 = 3 \times 5^2$

For each unique prime factor, choose the highest power that appears in the factorization of any of the numbers.
For 2: The highest power is $2^1$ (from 50). For 3: The highest power is $3^1$ (from 75). For 5: The highest power is $5^2$ (which appears in all three numbers).

Multiply these highest powers of all the unique prime factors to find the LCD.
$LCD = 2^1 \times 3^1 \times 5^2$

Calculate the LCD by multiplying the numbers.
$LCD = 2 \times 3 \times 25$

Perform the multiplication to find the LCD.
$LCD = 2 \times 3 \times 25 = 6 \times 25 = 150$
The least common denominator (LCD) of 25, 50, and 75 is 150.