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 $2^2 \, \times \, 5 = 4 \, \times \, 5 = 20$.

Let's try to find the lowest common denominator between 2 and 10

To find the lowest common denominator, we need to find a number that is divisible by both 2 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

$\frac{1\times5}{2\times5}+\frac{2\times1}{10\times1}=\frac{5}{10}+\frac{2}{10}$

Now we'll combine and get:

$\frac{5+2}{10}=\frac{7}{10}$

Let's try to find the least common denominator between 2 and 10

To find the least common denominator, we need to find a number that is divisible by both 2 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

$\frac{1\times5}{2\times5}+\frac{3\times1}{10\times1}=\frac{5}{10}+\frac{3}{10}$

Now we'll combine and get:

$\frac{5+3}{10}=\frac{8}{10}$

Let's try to find the lowest common denominator between 3 and 9

To find 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

Now we'll 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

$\frac{1\times3}{3\times3}+\frac{5\times1}{9\times1}=\frac{3}{9}+\frac{5}{9}$

Now we'll combine and get:

$\frac{3+5}{9}=\frac{8}{9}$

Let's try to find the lowest common denominator between 4 and 8

To find 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

Now we'll 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

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

Now we'll combine and get:

$\frac{2+4}{8}=\frac{6}{8}$

Let's try to find the least common denominator between 4 and 8

To find the least common denominator, we need to find a number that is divisible by both 4 and 8

In this case, the common denominator is 8

Now we'll 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

$\frac{1\times2}{4\times2}+\frac{6\times1}{8\times1}=\frac{2}{8}+\frac{6}{8}$

Now we'll combine and get:

$\frac{2+6}{8}=\frac{8}{8}=1$

Let's try to find the lowest common denominator between 5 and 15

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 15

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{5\times3}+\frac{2\times1}{15\times1}=\frac{3}{15}+\frac{2}{15}$

Now we'll combine and get:

$\frac{3+2}{15}=\frac{5}{15}$

Let's try to find the lowest common denominator between 5 and 15

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 15

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{3\times3}{5\times3}+\frac{2\times1}{15\times1}=\frac{9}{15}+\frac{2}{15}$

Now we'll combine and get:

$\frac{9+2}{15}=\frac{11}{15}$

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

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

Finally we'll combine and obtain the following:

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

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 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:

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

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:

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