What are the first 10 multiples of 6?
The concept of multiples of 6 is essential for mastering maths topics like factors, divisibility, and LCM. Understanding multiples helps students solve arithmetic problems faster and prepares them well for exams and real-life applications.
What Is Multiples of 6?
A multiple of 6 is any number you get when you multiply 6 by a whole (natural) number. For example, 6 × 1 = 6, 6 × 2 = 12, 6 × 3 = 18, and so on. This idea connects directly to the 6 times table, skip counting by 6, and checking divisibility by 6. Other maths concepts, like common multiples and LCM, also use multiples of 6 as a base.
Key Formula for Multiples of 6
Here’s the standard formula: \( \text{Multiple of 6} = 6 \times n \), where \( n \) is any whole number (1, 2, 3, ...).
Cross-Disciplinary Usage
Multiples of 6 are not only useful in Maths but also play a key role in patterns in Computer Science, grouping in everyday life, and reasoning in competitive exams. Students working on subjects like Physics or preparing for the JEE/NEET will often spot multiples and divisibility by 6 in questions on sequences, cycles, and grouping.
Step-by-Step Illustration
- To find if 48 is a multiple of 6:
Divide 48 by 6. \( 48 \div 6 = 8 \), which is a whole number. - To get the first five multiples of 6:
6 × 1 = 6
6 × 2 = 12
6 × 3 = 18
6 × 4 = 24
6 × 5 = 30
Speed Trick or Vedic Shortcut
A handy tip: Any multiple of 6 is always even and also divisible by 3. To quickly check if a number is a multiple of 6, see if it’s divisible by 2 (even number) and by 3 (sum of digits is divisible by 3).
Example Trick: Is 54 a multiple of 6?
- 54 is even (ends with 4).
- Sum the digits: 5 + 4 = 9. Since 9 is divisible by 3, 54 is a multiple of 6.
Shortcuts like these save time in MCQs and quick practice. Vedantu’s live classes share more such tricks to boost exam speed.
Comprehensive Table of Multiples of 6 up to 100
| n | Multiples of 6 |
|---|---|
| 1 | 6 |
| 2 | 12 |
| 3 | 18 |
| 4 | 24 |
| 5 | 30 |
| 6 | 36 |
| 7 | 42 |
| 8 | 48 |
| 9 | 54 |
| 10 | 60 |
| 11 | 66 |
| 12 | 72 |
| 13 | 78 |
| 14 | 84 |
| 15 | 90 |
| 16 | 96 |
Properties & Tricks for Multiples of 6
- Every multiple of 6 is also a multiple of 2 and 3.
- Multiples of 6 come in the sequence: 6, 12, 18, 24, ... (with a difference of 6 each time).
- Quick divisibility rule: A number is a multiple of 6 if it’s even AND its digits add up to a multiple of 3.
- Multiples of 6 are always even numbers.
Try These Yourself
- List the first ten multiples of 6.
- Is 72 a multiple of 6?
- Find all multiples of 6 between 30 and 60.
- Check if 40 is a multiple of 6.
- Write the next multiple of 6 after 84.
Solved Examples
- A girl makes necklaces, each with 6 beads more than the last. What is the number of beads in the 10th necklace?
1. First necklace: 6 beads
2. Sequence: 6, 12, 18, ...
3. 10th necklace: 6 × 10 = 60 beads
- Is 54 a multiple of 6?
1. 54 ÷ 6 = 9 (no remainder)
2. So YES, 54 is a multiple of 6.
- How many multiples of 6 are there from 1 to 100?
1. First multiple: 6
2. Last before 100: 96
3. Number of terms: (96 - 6) ÷ 6 + 1 = 16
- What’s the sum of the first five multiples of 6?
1. List: 6, 12, 18, 24, 30
2. Sum: 6 + 12 + 18 + 24 + 30 = 90
Frequent Errors and Misunderstandings
- Mixing up factors and multiples (they are NOT the same).
- Leaving out zero: zero is a multiple of every number, including 6.
- Confusing odd numbers as possible multiples of 6—they are always even.
Relation to Other Concepts
Multiples of 6 are closely related to factors, LCM, and multiples of other numbers like 4 and 8. Understanding them improves your skills in topics like divisibility, prime factorization, and pattern recognition.
Classroom Tip
An easy way to remember the first five multiples of 6 is to learn the 6 times table and practice skip counting: 6, 12, 18, 24, 30. Vedantu’s teachers often use colour-coded charts or rhythm games to help memorise multiples for quicker recall in exams.
We explored multiples of 6—from what they mean, how to find them, easy shortcuts, solved examples, and connections with other maths skills. Keep practicing with Vedantu and use these tricks to master maths topics and build confidence for all exams!
Related Topics for Practice: Multiples of 4 | Multiples of 8 | LCM | Factors and Multiples | Divisibility Rules
FAQs on Multiples of 6 Explained for Students
1. What are the first 10 multiples of 6?
The first ten multiples of 6 are obtained by multiplying 6 by the first ten natural numbers (1-10). They are: 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60.
2. How do you find the multiples of 6?
To find multiples of 6, you repeatedly add 6 to itself or, more efficiently, multiply 6 by any whole number (0, 1, 2, 3...). For example: 6 x 1 = 6, 6 x 2 = 12, 6 x 3 = 18, and so on.
3. What is the 100th multiple of 6?
The 100th multiple of 6 is calculated by multiplying 6 by 100. This equals 600.
4. How do you know if a number is a multiple of 6?
A number is a multiple of 6 if it is divisible by both 2 and 3 without leaving a remainder. You can check this by using the divisibility rules for 2 (even numbers) and 3 (sum of digits divisible by 3).
5. What are the multiples of 6 between 100 and 200?
The multiples of 6 between 100 and 200 are: 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198.
6. What are the first 20 multiples of 6?
The first twenty multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120.
7. What is the difference between factors and multiples of 6?
Factors of 6 are the numbers that divide 6 without a remainder (1, 2, 3, and 6). Multiples of 6 are the numbers obtained by multiplying 6 by any whole number (6, 12, 18, 24...). Factors are smaller than or equal to the number, while multiples are larger than or equal to the number.
8. Are all multiples of 6 even numbers?
Yes, all multiples of 6 are even numbers. This is because 6 itself is an even number (divisible by 2), and multiplying any number by an even number always results in an even number.
9. How are multiples of 6 used in finding the Least Common Multiple (LCM)?
When finding the LCM of a set of numbers, including 6, you identify the smallest number that is a multiple of all the numbers in the set. Listing multiples of each number can help determine the LCM.
10. Can you give a real-life example of multiples of 6?
Imagine you're arranging eggs in cartons that hold 6 eggs each. Each carton represents a multiple of 6: one carton is 6 eggs, two cartons are 12 eggs, three cartons are 18 eggs, and so on.
11. What pattern can be observed in the unit digits of multiples of 6?
The unit digits of multiples of 6 follow a pattern: 6, 2, 8, 4, 0, 6, 2, 8, 4, 0... This pattern repeats every five multiples.
12. What are some common multiples of 6 and 8?
Common multiples of 6 and 8 are numbers that are divisible by both 6 and 8. The first few are 24, 48, 72, and 96. These can be found by listing the multiples of each number and identifying the common ones.
