Common Denominators

A common denominator is a denominator that will be common and equal for all the fractions in the exercise. We will reach such a denominator by reducing or enlarging the fraction - an operation of multiplication or division.
We can arrive at several correct common denominators.

We will divide the search for the common denominator into 3 cases:

The first case: one of the denominators appearing in the original exercise will be the common denominator.
In this case, we will notice that we only have to multiply one denominator by an integer to reach the same denominator as in the other fraction.
The second case: find a number that both denominators in the exercise can reach by multiplication.
The third case: find the common denominator by multiplying the denominators.

Detailed explanation

Practice Common Denominators

Question 1

What is the least common multiple (LCM) of the numbers 3 and 7?

$\boxed 3~~~\boxed 7$

Question 2

You have two numbers, 4 and 6. What is their least common multiple?

$\boxed 4~~~\boxed 6$

Question 3

Find the least common multiple of 5 and 9.

$\boxed 5~~~\boxed 9$

Question 4

Determine the least common multiple of 8 and 12.

$\boxed 8~~~\boxed{ 12}$

Question 5

What is the least common multiple of the numbers 10 and 15?

$\boxed {10}~~~\boxed {15 }$

Examples with solutions for Common Denominators

Exercise #1

What is the least common multiple (LCM) of the numbers 3 and 7?

$\boxed 3~~~\boxed 7$

Step-by-Step Solution

To find the least common multiple (LCM) of the numbers 3 and 7, we will list the multiples of each number and find the smallest multiple they have in common.

Multiples of 3: $3, 6, 9, 12, 15, 18, 21, \ldots$

Multiples of 7: $7, 14, 21, 28, \ldots$

The smallest common multiple is $21$ .

Answer

Exercise #2

You have two numbers, 4 and 6. What is their least common multiple?

$\boxed 4~~~\boxed 6$

Step-by-Step Solution

To find the least common multiple (LCM) of the numbers 4 and 6, list the multiples of each number and find the smallest multiple they have in common.

Multiples of 4: $4, 8, 12, 16, \ldots$

Multiples of 6: $6, 12, 18, 24, \ldots$

The smallest common multiple is $12$ .

Answer

Exercise #3

Find the least common multiple of 5 and 9.

$\boxed 5~~~\boxed 9$

Step-by-Step Solution

To find the least common multiple (LCM) of 5 and 9, list the multiples of each number and find the smallest multiple they have in common.

Multiples of 5: $5, 10, 15, 20, 25, 30, 35, 40, 45, \ldots$

Multiples of 9: $9, 18, 27, 36, 45, \ldots$

The smallest common multiple is $45$ .

Answer

Exercise #4

Determine the least common multiple of 8 and 12.

$\boxed 8~~~\boxed{ 12}$

Step-by-Step Solution

To find the least common multiple (LCM) of the numbers 8 and 12, we will list the multiples of each number and find the smallest multiple they have in common.

Multiples of 8: $8, 16, 24, 32, \ldots$

Multiples of 12: $12, 24, 36, 48, \ldots$

The smallest common multiple is $24$ .

Answer

Exercise #5

What is the least common multiple of the numbers 10 and 15?

$\boxed {10}~~~\boxed {15 }$

Step-by-Step Solution

To find the least common multiple (LCM) of 10 and 15, list the multiples of each number and find the smallest multiple they have in common.

Multiples of 10: $10, 20, 30, 40, \ldots$

Multiples of 15: $15, 30, 45, 60, \ldots$

The smallest common multiple is $30$ .

Answer

Question 1

You have a pair of denominators, what is their least common multiple?

$\boxed 3~~~\boxed 4$

Question 2

You have a pair of denominators, what is their least common multiple?

$\boxed 6~~~\boxed 8$

Question 3

You have a pair of denominators, what is their least common multiple?

$\boxed 7~~~\boxed 5$

Question 4

You have a pair of denominators, what is their least common multiple?

$\boxed 9~~~\boxed 6$

Question 5

What is the least common multiple of these two numbers?

$\boxed{2}~~~\boxed{5}$

Exercise #6

You have a pair of denominators, what is their least common multiple?

$\boxed 3~~~\boxed 4$

Step-by-Step Solution

To find the least common multiple (LCM) of $3$ and $4$ , we list the multiples of each number until we find the smallest multiple they have in common.

Multiples of $3$ : $3, 6, 9, 12, 15, \ldots$

Multiples of $4$ : $4, 8, 12, 16, 20, \ldots$

The smallest common multiple is $12$ .

Answer

Exercise #7

You have a pair of denominators, what is their least common multiple?

$\boxed 6~~~\boxed 8$

Step-by-Step Solution

To find the least common multiple (LCM) of $6$ and $8$ , list the multiples of each number until the smallest common multiple appears.

Multiples of $6$ : $6, 12, 18, 24, 30, \ldots$

Multiples of $8$ : $8, 16, 24, 32, 40, \ldots$

The smallest common multiple is $24$ .

Answer

Exercise #8

You have a pair of denominators, what is their least common multiple?

$\boxed 7~~~\boxed 5$

Step-by-Step Solution

To determine the least common multiple (LCM) of $7$ and $5$ , we list the multiples of each number.

Multiples of $7$ : $7, 14, 21, 28, 35, \ldots$

Multiples of $5$ : $5, 10, 15, 20, 25, 30, 35, \ldots$

The smallest common multiple is $35$ .

Answer

Exercise #9

You have a pair of denominators, what is their least common multiple?

$\boxed 9~~~\boxed 6$

Step-by-Step Solution

To find the least common multiple (LCM) of $9$ and $6$ , list the multiples of each number until the smallest common multiple appears.

Multiples of $9$ : $9, 18, 27, 36, \ldots$

Multiples of $6$ : $6, 12, 18, 24, 30, \ldots$

The smallest common multiple is $18$ .

Answer

Exercise #10

What is the least common multiple of these two numbers?

$\boxed{2}~~~\boxed{5}$

Step-by-Step Solution

To find the least common multiple (LCM) of $2$ and $5$ , we list the multiples of each number:

Multiples of $2$ are $2, 4, 6, 8, 10, \ldots$
Multiples of $5$ are $5, 10, 15, \ldots$

The smallest common multiple is $10$ .

Answer

Question 1

What is the least common multiple of these two numbers?

$\boxed{3}~~~\boxed{9}$

Question 2

What is the least common multiple of these two numbers?

$\boxed{4}~~~\boxed{8}$

Question 3

What is the least common multiple of these two numbers?

$\boxed{6}~~~\boxed{9}$

Question 4

What is the least common multiple of these two numbers?

$\boxed{5}~~~\boxed{10}$

Question 5

What is the least common multiple of these two numbers?

$\boxed{7}~~~\boxed{14}$

Exercise #11

What is the least common multiple of these two numbers?

$\boxed{3}~~~\boxed{9}$

Step-by-Step Solution

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 $9$ .

Answer

Exercise #12

What is the least common multiple of these two numbers?

$\boxed{4}~~~\boxed{8}$

Step-by-Step Solution

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 $8$ .

Answer

Exercise #13

What is the least common multiple of these two numbers?

$\boxed{6}~~~\boxed{9}$

Step-by-Step Solution

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 $18$ .

Answer

Exercise #14

What is the least common multiple of these two numbers?

$\boxed{5}~~~\boxed{10}$

Step-by-Step Solution

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 $10$ .

Answer

Exercise #15

What is the least common multiple of these two numbers?

$\boxed{7}~~~\boxed{14}$

Step-by-Step Solution

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 $14$ .

Common Denominators - Examples, Exercises and Solutions

We will divide the search for the common denominator into 3 cases:

Suggested Topics to Practice in Advance

Practice Common Denominators

Examples with solutions for Common Denominators

Exercise #1

Step-by-Step Solution

Answer

Exercise #2

Step-by-Step Solution

Answer

Exercise #3

Step-by-Step Solution

Answer

Exercise #4

Step-by-Step Solution

Answer

Exercise #5

Step-by-Step Solution

Answer

Exercise #6

Step-by-Step Solution

Answer

Exercise #7

Step-by-Step Solution

Answer

Exercise #8

Step-by-Step Solution

Answer

Exercise #9

Step-by-Step Solution

Answer

Exercise #10

Step-by-Step Solution

Answer

Exercise #11

Step-by-Step Solution

Answer

Exercise #12

Step-by-Step Solution

Answer

Exercise #13

Step-by-Step Solution

Answer

Exercise #14

Step-by-Step Solution

Answer

Exercise #15

Step-by-Step Solution

Answer

More Questions

Topics learned in later sections