How to Find and Use Multiples of 12 in Maths
The concept of multiples of 12 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding multiples of 12 can help you solve questions about LCM, number patterns, and quick mental math in school, Olympiads, and competitive tests. Vedantu covers these concepts in step-by-step detail to help students learn quickly and confidently.
What Is Multiples of 12?
A multiple of 12 is any number that can be written as 12 multiplied by a whole number (for example, 12 × 1, 12 × 2, 12 × 3, and so on). You’ll find this concept applied in areas such as divisibility rules, times tables, and finding the least common multiple (LCM).
Key Formula for Multiples of 12
Here’s the standard formula: \( 12 \times n \), where n is any whole number (n = 0, 1, 2, 3, ...).
Why Learn Multiples of 12?
Multiples of 12 are not only useful in Maths but also play an important role in Physics, Computer Science, and daily mental calculations. Knowing these lets you quickly find common time intervals (hours and months), solve LCM and HCF questions, and confidently answer MCQs in exams. Students preparing for JEE or NEET will see its relevance in various problem-solving situations.
Step-by-Step: How to Find Multiples of 12
- Start with the number 12.
12 × 1 = 12
- Keep multiplying 12 by 2, 3, 4, and so on.
12 × 2 = 24
12 × 3 = 36
12 × 4 = 48 - Write down each answer. These are your multiples of 12.
First 20 Multiples of 12 (Quick Reference Table)
| n | 12 × n | Multiple |
|---|---|---|
| 1 | 12 × 1 | 12 |
| 2 | 12 × 2 | 24 |
| 3 | 12 × 3 | 36 |
| 4 | 12 × 4 | 48 |
| 5 | 12 × 5 | 60 |
| 6 | 12 × 6 | 72 |
| 7 | 12 × 7 | 84 |
| 8 | 12 × 8 | 96 |
| 9 | 12 × 9 | 108 |
| 10 | 12 × 10 | 120 |
| 11 | 12 × 11 | 132 |
| 12 | 12 × 12 | 144 |
| 13 | 12 × 13 | 156 |
| 14 | 12 × 14 | 168 |
| 15 | 12 × 15 | 180 |
| 16 | 12 × 16 | 192 |
| 17 | 12 × 17 | 204 |
| 18 | 12 × 18 | 216 |
| 19 | 12 × 19 | 228 |
| 20 | 12 × 20 | 240 |
Tricks for Multiples of 12
Speed Trick: Since 12 = 3 × 4, a number is a multiple of 12 if it is divisible by both 3 and 4. For quick checking in exams, add up the digits (divisible by 3) and check last two digits for divisibility by 4.
Example: Is 336 a multiple of 12?
3+3+6=12 (divisible by 3), last two digits 36 (divisible by 4). Yes, so 336 is a multiple of 12.
Key Properties of Multiples of 12
- All multiples of 12 are even numbers
- Each multiple is a product of 12 and a whole number
- There are infinite multiples of 12
- If a number is a multiple of 12, it will also be a multiple of 3, 4, and 6
Multiples of 12 vs. Factors of 12
| Multiples of 12 | Factors of 12 |
|---|---|
| Numbers like 12, 24, 36, 48, 60, etc (goes on infinitely) | Numbers like 1, 2, 3, 4, 6, and 12 (fixed, always fewer) |
| Obtained by multiplying 12 by other numbers | Numbers which divide 12 exactly |
For a deep dive into factors, check Factors of 12.
Applications and Word Problems Involving Multiples of 12
Multiples of 12 are helpful in time calculations, grouping, arranging objects, finding LCM, and solving puzzles. For example:
If you want to divide 60 chocolates equally among friends, you look for the closest multiple of 12 less than 60 to know how many can be equally shared.
Competitive exams often use such logic in their questions, and Vedantu’s live classes teach these with practical examples.
Try These Yourself
- Write the first five multiples of 12.
- Check if 96 is a multiple of 12.
- List all multiples of 12 between 50 and 120.
- Is every multiple of 6 also a multiple of 12?
Frequent Errors and Misunderstandings
- Confusing multiples of 12 with factors of 12
- Missing that multiples can go on infinitely
- Only adding 12 repeatedly, forgetting multiplication
Links to Related Maths Concepts
Summary: What to Remember About Multiples of 12
- Multiples of 12 are infinite: 12, 24, 36, 48, ...
- Formula: 12 × n (n=whole number)
- Used in LCM, grouping, time, and patterns
- All multiples of 12 are even and divisible by both 3 and 4
We explored multiples of 12—from definition and formula to quick tricks, tables, and word problems. Keep practicing with Vedantu to master the concept and become confident at solving problems using multiples in maths!
FAQs on Multiples of 12 Explained with Charts & Easy Examples
1. What are the multiples of 12?
Multiples of 12 are numbers obtained by multiplying 12 by any whole number. They can be expressed as 12n, where 'n' represents any whole number (0, 1, 2, 3, and so on). The first few multiples of 12 are 0, 12, 24, 36, 48, 60, and so on.
2. How do you find multiples of 12?
To find multiples of 12, simply multiply 12 by consecutive whole numbers. You can also use skip-counting: start at 12 and repeatedly add 12. For example: 12 × 1 = 12, 12 × 2 = 24, 12 × 3 = 36, and so forth.
3. What are the first 10 multiples of 12?
The first ten multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120.
4. How many multiples of 12 are there between 1 and 100?
There are eight multiples of 12 between 1 and 100: 12, 24, 36, 48, 60, 72, 84, and 96.
5. What are the common multiples of 12 and 8?
Common multiples of 12 and 8 are numbers that are multiples of both 12 and 8. The first few common multiples are: 24, 48, 72, 96, and so on. To find them, you can list the multiples of each number and identify the ones they share.
6. Is 72 a multiple of 12?
Yes, 72 is a multiple of 12 because 12 × 6 = 72.
7. What is the 12th multiple of 12?
The 12th multiple of 12 is 12 x 12 = 144.
8. How can multiples of 12 help in solving LCM and HCF questions?
Understanding multiples is crucial for finding the Least Common Multiple (LCM) and Highest Common Factor (HCF) of numbers. To find the LCM, you identify the smallest multiple common to both numbers. For HCF, you look for the largest number that divides both without a remainder. Listing multiples can help you find these quickly.
9. What is the difference between multiples and factors of 12?
Multiples of 12 are numbers that result from multiplying 12 by a whole number (e.g., 24, 36, 48). Factors of 12 are whole numbers that divide 12 without a remainder (e.g., 1, 2, 3, 4, 6, 12). A number is a factor of its multiples.
10. Are all multiples of 6 also multiples of 12?
No, not all multiples of 6 are also multiples of 12. For example, 6, 18, 30 are multiples of 6 but not multiples of 12. Only those multiples of 6 which are even multiples of 6 will also be multiples of 12.
11. What are some real-world applications of understanding multiples of 12?
Understanding multiples of 12 is useful in various everyday situations. For instance, it helps in tasks involving grouping items into dozens (12), calculating costs based on dozen pricing, and in time-related calculations (12 hours on a clock face). It is also useful in calculating areas of objects with dimensions that are multiples of 12.
12. Why are multiples of 12 always even numbers?
Multiples of 12 are always even because 12 itself is an even number (it's divisible by 2). When you multiply an even number by any whole number, the result is always even.
