Common Denominators: One of the denominators is the common denominator

To find the least common multiple (LCM) of $10$ and $15$, we list the multiples of each number:

• Multiples of $10$ are $10, 20, 30, 40, \ldots$
• Multiples of $15$ are $15, 30, 45, \ldots$

The smallest common multiple is $30$.

To find the least common multiple (LCM) of $3$ and $9$, we list the multiples of each number:

• Multiples of $3$ are $3, 6, 9, 12, 15, \ldots$
• Multiples of $9$ are $9, 18, 27, \ldots$

The smallest common multiple is $9$.

To find the least common multiple (LCM) of $4$ and $8$, we list the multiples of each number:

• Multiples of $4$ are $4, 8, 12, 16, 20, \ldots$
• Multiples of $8$ are $8, 16, 24, \ldots$

The smallest common multiple is $8$.

To find the least common multiple (LCM) of $5$ and $10$, we list the multiples of each number:

• Multiples of $5$ are $5, 10, 15, 20, \ldots$
• Multiples of $10$ are $10, 20, 30, \ldots$

The smallest common multiple is $10$.

To find the least common multiple (LCM) of $6$ and $9$, we list the multiples of each number:

• Multiples of $6$ are $6, 12, 18, 24, \ldots$
• Multiples of $9$ are $9, 18, 27, \ldots$

The smallest common multiple is $18$.

To find the least common multiple (LCM) of $7$ and $14$, we list the multiples of each number:

• Multiples of $7$ are $7, 14, 21, 28, \ldots$
• Multiples of $14$ are $14, 28, 42, \ldots$

The smallest common multiple is $14$.

To find the least common multiple (LCM) of $8$ and $12$, we list the multiples of each number:

• Multiples of $8$ are $8, 16, 24, 32, \ldots$
• Multiples of $12$ are $12, 24, 36, \ldots$

The smallest common multiple is $24$.

To find the least common multiple (LCM) of $5$, $10$, and $20$, find their prime factorizations:

$5 = 5$

$10 = 2 \, \times \, 5$

$20 = 2^2 \, \times \, 5$

$\times$The LCM is determined by selecting the greatest power of each prime number:

$2^2$ from 20 and $5$.

The LCM is $2^2 \, \times \, 5 = 4 \, \times \, 5 = 20$.

We must first identify the lowest common denominator between 4 and 8.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 8.

In this case, the common denominator is 8.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 8.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{1\times2}{4\times2}+\frac{5\times1}{8\times1}=\frac{2}{8}+\frac{5}{8}$

Finally we'll combine and obtain the following:

$\frac{2+5}{8}=\frac{7}{8}$

Let's first identify the lowest common denominator between 4 and 2.

In order to identify the lowest common denominator, we need to find a number that is divisible by both 4 and 2.

In this case, the common denominator is 4

We will then proceed to multiply each fraction by the appropriate number in order to reach the denominator 4

We'll multiply the first fraction by 1

We'll multiply the second fraction by 2

$\frac{2\times1}{4\times1}+\frac{1\times2}{2\times2}=\frac{2}{4}+\frac{2}{4}$

Finally we will combine and obtain the following:

$\frac{2+2}{4}=\frac{4}{4}=1$

Let's first identify the lowest common denominator between 2 and 8.

In order to determine the lowest common denominator, we need to first find a number that is divisible by both 2 and 8.

In this case, the common denominator is 8.

We'll then proceed to multiply each fraction by the appropriate number in order to reach the denominator 8.

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

$\frac{1\times4}{2\times4}+\frac{3\times1}{8\times1}=\frac{4}{8}+\frac{3}{8}$

Finally we'll combine and obtain the following:

$\frac{4+3}{8}=\frac{7}{8}$

We must first identify the lowest common denominator between 3 and 9.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 9.

In this case, the common denominator is 9.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 9.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{3\times3}+\frac{4\times1}{9\times1}=\frac{3}{9}+\frac{4}{9}$

Finally we'll combine and obtain the following:

$\frac{3+4}{9}=\frac{7}{9}$

Let's begin by identifying the lowest common denominator between 3 and 6.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 6.

In this case, the common denominator is 6.

Let's proceed to multiply each fraction by the appropriate number in order to reach the denominator 6.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{2\times2}{3\times2}+\frac{1\times1}{6\times1}=\frac{4}{6}+\frac{1}{6}$

Finally we'll combine and obtain the following result:

$\frac{4+1}{6}=\frac{5}{6}$

We must first identify the lowest common denominator between 4 and 8

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 8.

In this case, the common denominator is 8.

We will proceed to multiply each fraction by the appropriate number to reach the denominator 8.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{2\times2}{4\times2}+\frac{1\times1}{8\times1}=\frac{4}{8}+\frac{1}{8}$

Finally we'll combine and obtain the following:

$\frac{4+1}{8}=\frac{5}{8}$

We must first identify the lowest common denominator between 5 and 10.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 5 and 10.

In this case, the common denominator is 10.

We will proceed to multiply each fraction by the appropriate number to reach the denominator 10.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{1\times2}{5\times2}+\frac{6\times1}{10\times1}=\frac{2}{10}+\frac{6}{10}$

Finally we'll combine and obtain the following:

$\frac{2+6}{10}=\frac{8}{10}$

We must first identify the lowest common denominator between 3 and 6.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 6.

In this case, the common denominator is 6.

We'll then proceed to multiply each fraction by the appropriate number to reach the denominator 6.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{1\times2}{3\times2}+\frac{3\times1}{6\times1}=\frac{2}{6}+\frac{3}{6}$

Finally we'll combine and obtain the following:

$\frac{2+3}{6}=\frac{5}{6}$

We must first identify the lowest common denominator between 4 and 8.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 8.

In this case, the common denominator is 8.

We'll then proceed to multiply each fraction by the appropriate number to reach the denominator 8.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{3\times2}{4\times2}+\frac{1\times1}{8\times1}=\frac{6}{8}+\frac{1}{8}$

Finally we'll combine and obtain the following:

$\frac{6+1}{8}=\frac{7}{8}$

We must first identify the lowest common denominator between 4 and 12.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 12.

In this case, the common denominator is 12.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 12.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{4\times3}+\frac{6\times1}{12\times1}=\frac{3}{12}+\frac{6}{12}$

Finally we'll combine and obtain the following:

$\frac{3+6}{12}=\frac{9}{12}$

We must first identify the lowest common denominator between 6 and 12.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 6 and 12.

In this case, the common denominator is 12.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 12.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{2\times2}{6\times2}+\frac{4\times1}{12\times1}=\frac{4}{12}+\frac{4}{12}$

Finally we'll combine and obtain the following:

$\frac{4+4}{12}=\frac{8}{12}$

We must first identify the lowest common denominator between 3 and 9.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 9.

In this case, the common denominator is 9.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 9.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{3\times3}+\frac{2\times1}{9\times1}=\frac{2}{9}+\frac{2}{9}$

Finally we'll combine and obtain the following:

$\frac{2+3}{9}=\frac{5}{9}$