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103 LearnersLast updated on March 29th, 2025
Multiples of 12
In math, multiples are the products we get while multiplying a number with other numbers. Multiples play a key role in construction and design, counting groups of items, sharing resources equally, and managing time effectively. In this topic, we will learn the essential concepts of multiples of 12.
What are the Multiples of 12?
Now, let us learn more about multiples of 12. Multiples of 12 are the numbers you get when you multiply 12 by any whole number, including zero. Each number has an infinite number of multiples, including a multiple of itself. A multiple of 12 can be denoted as 12 × n, where ‘n’ represents any whole number (0, 1, 2, 3,…). So, we can summarize that:
Multiple of a number = Number × Any whole number
For example, multiplying 12 × 1 will give us 12 as the product. Multiples of 12 will be larger or equal to 12.
List of First 20 Multiples of 12
Multiples of 12 include the products of 12 and an integer. Multiples of 12 are divisible by 12 evenly. The first few multiples of 12 are given below:
| TABLE OF 12 (1-10) | |
|---|---|
|
12 x 1 = 12 |
12 x 6 = 72 |
|
12 x 2 = 24 |
12 x 7 = 84 |
|
12 x 3 = 36 |
12 x 8 = 96 |
|
12 x 4 = 48 |
12 x 9 = 108 |
|
12 x 5 = 60 |
12 x 10 = 120 |
| TABLE OF 12 (11-20) | |
|---|---|
|
12 x 11 = 132 |
12 x 16 = 192 |
|
12 x 12 = 144 |
12 x 17 = 204 |
|
12 x 13 = 156 |
12 x 18 = 216 |
|
12 x 14 = 168 |
12 x 19 = 228 |
|
12 x 15 = 180 |
12 x 20 = 240 |
Now, we know the first few multiples of 12. They are 0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120,...
Operations with Multiples of 12
Understanding the multiples of 12 helps solve mathematical problems and boost our multiplication and division skills. When working with multiples of 12, we apply them to different mathematical operations such as addition, subtraction, multiplication, and division.
Sum of First 5 Multiples of 12:
12, 24, 36, 48, and 60 are the first five multiples of 12. When multiplying 12 from 1 to 5 we get these numbers as the products.
So, the sum of these multiples is:
12 + 24 + 36 + 48 + 60 = 180
When we add the first 5 multiples of 12, the answer will be 180.
Subtraction of First 5 Multiples of 12:
While we do subtraction, it improves our comprehension of how the value decreases when each multiple is subtracted from the previous one. 12, 24, 36, 48, and 60 are the first five multiples of 12. So, let us calculate it as given below:
12 - 24 = -12
-12 - 36 = -48
-48 - 48 = -96
-96 - 60 = -156
Hence, the result of subtracting the first 5 multiples of 12 is -156.
Average of First 5 Multiples of 12:
To calculate the average, we need to identify the sum of the first 5 multiples of 12, and then divide it by the count, i.e., 5. Because there are 5 multiples presented in the calculation. Averaging helps us to understand the concepts of central tendencies and other values. We know the sum of the first 5 multiples of 12 is 180.
12 + 24 + 36 + 48 + 60 = 180
Next, divide the sum by 5:
180 ÷ 5 = 36
36 is the average of the first 5 multiples of 12.
Product of First 5 Multiples of 12:
The product of given numbers is the result of multiplying all of them together. Here, the first 5 multiples of 12 include 12, 24, 36, 48, and 60. Now, the product of these numbers is:
12 × 24 × 36 × 48 × 60 = 29,937,792
The product of the first 5 multiples of 12 is 29,937,792.
Division of First 5 Multiples of 12:
While we perform division, we get to know how many times 12 can fit into each of the given multiples. 12, 24, 36, 48, and 60 are the first 5 multiples of 12.
12 ÷ 12 = 1
24 ÷ 12 = 2
36 ÷ 12 = 3
48 ÷ 12 = 4
60 ÷ 12 = 5
The results of dividing the first 5 multiples of 12 are: 1, 2, 3, 4, and 5.
Common Mistakes and How to Avoid Them in Multiples of 12
While working with multiples of 12, we make common mistakes. Identifying these errors and understanding how to avoid them can be helpful. Below are some frequent mistakes and tips to avoid them:
Mistake 1
Confusing Multiples with Factors
Sometimes, students get confused between the multiples and factors of 12. A simple trick to differentiate between the two is to remember that multiples are the products of multiplication, while factors are the divisors of the number. Multiples of 12 refer to the products we get while multiplying 12 with other numbers. For example, multiples of 12 include 0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, etc.
The factors of 12 are 1, 2, 3, 4, 6, and 12. When 12 is divided by these numbers, the remainder will be zero. These are the factors of 12, meaning that these numbers can divide 12 without any remainder.
Factors of 12:
12 ÷ 1 = 12
12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 4 = 3
12 ÷ 6 = 2
12 ÷ 12 = 1
Multiples of 12 Examples
Problem 1
Emma is organizing a charity marathon where participants run in groups. Each group consists of 12 runners. If the marathon is held over 5 weekends, and each weekend 12 new groups join, how many runners will participate in total?
720 runners
Explanation
Each weekend, 12 groups of runners join the marathon. To find the total number of runners, multiply the number of groups by the number of runners per group, and then multiply by the number of weekends.
Groups per weekend = 12
Runners per group = 12
Number of weekends = 5
12 × 12 × 5 = 720
Therefore, there will be a total of 720 runners participating.
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Problem 2
Liam is setting up a series of art exhibitions. Each exhibition displays the number of paintings equal to the first three multiples of 12. How many paintings are displayed in total across the three exhibitions?
72 paintings
Explanation
The first three multiples of 12 are 12, 24, and 36. Each exhibition displays these multiples of paintings.
First exhibition: 12 paintings
Second exhibition: 24 paintings
Third exhibition: 36 paintings
Total paintings = 12 + 24 + 36 = 72
Thus, there are 72 paintings displayed in total.
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Problem 3
In a music school, there are 12 practice rooms. Each room is occupied by 12 students during a music session. How many students are present in total during each session?
144 students
Explanation
To find the total number of students, multiply the number of practice rooms by the number of students in each room.
Number of practice rooms = 12
Number of students in each room = 12
12 × 12 = 144
Therefore, there are 144 students present during each session.
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Problem 4
Leo is arranging his collection of toy cars. He places them in rows of 12. If he has 6 rows of toy cars, how many toy cars does he have in total?
72 toy cars
Explanation
To determine the total number of toy cars, multiply the number of rows by the number of cars in each row.
Number of rows = 6
Number of cars in each row = 12
6 × 12 = 72
Hence, Leo has a total of 72 toy cars.
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Problem 5
Sophia is stacking boxes in her store. She stacks 12 boxes in the first stack, 24 boxes in the second stack, and 36 boxes in the third stack. How many boxes are there in total?
72 boxes
Explanation
The first stack has 12 boxes, the second stack has 24 boxes, and the third stack has 36 boxes. To find the total number of boxes:
12 + 24 + 36 = 72
Therefore, there are a total of 72 boxes in the store.
FAQs on Multiples of 12
1.How do you find the multiples of 12?
2.What is the LCM of 9 and 12?
3.What are the real-life applications of Multiples of 12?
4.Are multiples of 12 finite or infinite?
5.Is there any odd multiple of 12?
Important Glossaries for Multiples of 12
- Multiple: A multiple represents the product of a number that may be multiplied by an integer. For example, multiples of 12 include 12, 24, 36, 48, etc.
- Number pattern: This refers to how numbers are listed. It should follow a certain sequence. Multiples of 12 are the numbers that consist of the number pattern of 12.
- Even number: An even number refers to any number that can be divisible by 2 without leaving any remainder. The last digits of even numbers are 0, 2, 4, 6, or 8. All multiples of 12 are even numbers.
- Divisor: It refers to any number by which another number can be divided without leaving any remainder. 1, 2, 3, 4, 6, and 12 are the divisors of 12.
- Least Common Multiple (LCM): The smallest multiple that is common between two or more numbers. For example, the LCM of 9 and 12 is 36.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
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