Understanding the multiples of 12 is key to mastering multiplication and recognizing number patterns. Whether you’re a student learning your times tables or someone revisiting the topic, the 12 times table plays a vital role in various mathematical concepts.
In this guide, we’ll explore the multiples of 12 and provide clear examples to help you grasp the concept. By the end, you’ll understand the 12 times table and its practical uses.
What Are the Multiples of 12?
Every non-zero number has an infinite number of multiples. Additionally, each multiple of a non-zero number is either greater than or equal to the original number. Multiples of 12 are the numbers you get when you multiply 12 by any whole number. In other words, they form a sequence that starts at 12 and continues indefinitely by adding 12 each time. The first five multiples of 12 are 12, 24, 36, 48, and 60.
The 12 times table can be written as:
| 12 × 1 = 12 |
| 12 × 2 = 24 |
| 12 × 3 = 36 |
| 12 × 4 = 48 |
| 12 × 5 = 60 |
| 12 × 6 = 72 |
| 12 × 7 = 84 |
| 12 × 8 = 96 |
| 12 × 9 = 108 |
| 12 × 10 = 120 |
Here is the multiplication table of 12. So, the first 10 multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, and 120. As you can see, the multiples of 12 increase by 12 with each step. They are often used in real-life scenarios, such as calculating time (12 hours on a clock), understanding units of measurement, and solving problems involving groups or quantities.
How to Find the Multiples of 12?
Finding the multiples of a number is a simple process that involves multiplication. There are two primary methods you can use to find the multiples of a number:
1. Multiplying the Number by Whole Numbers
This is the most straightforward method. To find the multiples of a number, you simply multiply it by consecutive whole numbers (1, 2, 3, 4, and so on). The result of each multiplication is a multiple of the number.
Example: To find the multiples of 12, you multiply 12 by 1, 2, 3, 4, etc.:
- 12 × 1 = 12
- 12 × 2 = 24
- 12 × 3 = 36
- 12 × 4 = 48
- 12 × 5 = 60
- And so on…
2. Using Addition to Find Multiples
Alternatively, you can find the multiples of a number by repeatedly adding that number to itself. Each time you add the number to the previous multiple, you get the next multiple in the sequence.
Example: To find the first few multiples of 12, start with 12 and repeatedly add 12:
- Start with 12: 12
- Add 12: 12 + 12 = 24
- Add 12 again: 24 + 12 = 36
- Add 12 again: 36 + 12 = 48
- All the multiples of 12 are: 60, 72, 84, etc.
Both methods will give you the same result, so you can choose the one that works best for you depending on the situation.
Thus, the factors of 12 are: 1, 2, 3, 4, 6, and 12. These are the numbers that divide 12 evenly. In other words, 12 is divisible by 1, 2, 3, 4, 6, and 12 without any remainder. There can be infinite multiples of a number, whereas the factors are finite.
Solved Examples
1. Is 96 a multiple of 12? If yes, which multiple?
Solution: To check if 96 is a multiple of 12, divide 96 by 12:
96÷12=8
Since 96 divided by 12 gives a whole number (8), it is indeed a multiple of 12.
So, 96 is the 8th multiple of 12.
2. Word Problem
A factory packs chocolates into boxes of 12. If they pack 15 boxes of chocolates for a store, how many chocolates are packed in total?
Solution: To find the total number, multiply the number of boxes (15) by 12:
12×15=180
So, the factory packs 180 chocolates in total.
3. Multiples of Other Numbers:
- Multiples of 1:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10,… - Multiples of 2:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20,… - Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30,… - Multiples of 4:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40,… - Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50,… - Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60,… - Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70,… - Multiples of 8:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80,…
Conclusion
In this article, we explored the multiples of 12, from basic knowledge to practical applications. We provided detailed explanations on how to find multiples of 12 through multiplication and addition and included several problems to enhance understanding.
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Q1: What is the least common multiple of 8 and 12?
Answer: The least common multiple is the smallest of the multiples that the pair of given numbers have in common. To find the least common multiple (LCM) of 8 and 12, we first list the multiples of each number:
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, …
- Multiples of 12: 12, 24, 36, 48, 60, 72, …
The smallest number that appears in both lists is 24. Thus, the LCM of 8 and 12 is 24.
Q2: What are the common multiples of 9 and 12?
Answer:
- Multiples of 9: 9, 18, 27, 36, 45, 54,…
- Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120,…
So, the common multiples of 9 and 12 are 36, 72, 108, 144, and so on.
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