How to Check if a Number is a Multiple of 15
The concept of multiples of 15 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding and quickly identifying multiples of 15 can help students solve problems involving least common multiples (LCM), divisibility, and patterns, especially in competitive exams and quick calculations.
What Is a Multiple of 15?
A multiple of 15 is defined as any number which can be exactly divided by 15, or more precisely, a number that can be written as 15 × n, where n is a natural number (1, 2, 3, ...). You’ll find this concept applied in LCM, finding common multiples, word problems, and in recognizing arithmetic patterns in maths.
Key Formula for Multiples of 15
Here’s the standard formula: \( \text{Multiple of 15} = 15 \times n \), where n = 1, 2, 3, and so on.
List of Multiples of 15 (Up to 20)
Below is a quick-reference table that lists the first 20 multiples of 15. Students often memorize this table for mental maths and speedy calculations:
| n | 15 × n | Result |
|---|---|---|
| 1 | 15 × 1 | 15 |
| 2 | 15 × 2 | 30 |
| 3 | 15 × 3 | 45 |
| 4 | 15 × 4 | 60 |
| 5 | 15 × 5 | 75 |
| 6 | 15 × 6 | 90 |
| 7 | 15 × 7 | 105 |
| 8 | 15 × 8 | 120 |
| 9 | 15 × 9 | 135 |
| 10 | 15 × 10 | 150 |
| 11 | 15 × 11 | 165 |
| 12 | 15 × 12 | 180 |
| 13 | 15 × 13 | 195 |
| 14 | 15 × 14 | 210 |
| 15 | 15 × 15 | 225 |
| 16 | 15 × 16 | 240 |
| 17 | 15 × 17 | 255 |
| 18 | 15 × 18 | 270 |
| 19 | 15 × 19 | 285 |
| 20 | 15 × 20 | 300 |
How to Check If a Number is a Multiple of 15
You can check if a number is a multiple of 15 in two quick steps:
- Check if the number is divisible by 5 (number ends in 0 or 5).
- Check if the sum of its digits is divisible by 3.
If both conditions are true, the number is a multiple of 15.
Example: Is 90 a multiple of 15?
- It ends with 0 ➔ divisible by 5.
- 9+0=9 ➔ 9 is divisible by 3.
- Therefore, 90 is a multiple of 15.
Properties and Patterns of Multiples of 15
- Every multiple of 15 is also a multiple of 3 and 5.
- The difference between two successive multiples is always 15.
- Multiples alternate between numbers ending in 5 and 0.
- Each multiple forms an arithmetic sequence (15, 30, 45, ...).
- Multiples of 15 are infinite.
Multiples of 15 in Word Problems
Let’s solve two common word problems using multiples of 15.
Example 1: Find the 8th multiple of 15.
Using the formula:
1. \( 15 \times 8 = 120 \)2. So, the 8th multiple of 15 is 120.
Example 2: What is the least common multiple (LCM) of 15 and 10?
1. List multiples of 10: 10, 20, 30, 40, 50, 60, ...2. List multiples of 15: 15, 30, 45, 60, ...
3. First common multiple is 30.
4. So, LCM of 15 and 10 is 30.
Multiples vs Factors of 15
| Multiples of 15 | Factors of 15 |
|---|---|
| 15, 30, 45, 60, 75, ... (infinite) | 1, 3, 5, 15 (finite) |
| Obtained by multiplying 15 by whole numbers | Obtained by dividing 15 by whole numbers |
Speed Trick or Vedic Shortcut
A quick way to make sure a number is a multiple of 15 is to check if it ends with 0 or 5 (for 5), then add the digits and see if the sum is divisible by 3. Students use this divisibility shortcut for fast calculations in exams and MCQs.
Try These Yourself
- Write the first five multiples of 15.
- Is 225 a multiple of 15?
- Find all multiples of 15 between 50 and 100.
- Identify which of the following are not multiples of 15: 30, 33, 45, 53.
Frequent Errors and Misunderstandings
- Assuming multiples and factors mean the same (they are different!).
- Forgetting that every multiple of 15 is also a multiple of 3 and 5.
- Missing tricky cases where a number is a multiple of 5 but not 15.
Relation to Other Concepts
The idea of multiples of 15 connects closely with topics such as LCM and HCF. Mastering multiples helps you break down problems involving time intervals, cycles, and working with fractions or ratio.
Classroom Tip
A quick way to remember multiples of 15 is by noting every fifth multiple of 3 (15, 30, 45, ...), or by using the 15 times table. Vedantu’s teachers often visualize this with number charts to build recall in live sessions.
We explored multiples of 15—from definition, formula, properties, examples, common mistakes, and how they are related to factors and LCM. Continue practicing with Vedantu to become confident in solving maths problems using this concept. For similar topics, you can also browse the multiples overview page.
Related Vedantu Pages
FAQs on Multiples of 15 Explained with Easy Methods and Examples
1. What are the first 10 multiples of 15?
The first ten multiples of 15 are obtained by multiplying 15 by each whole number from 1 to 10. They are: 15, 30, 45, 60, 75, 90, 105, 120, 135, and 150.
2. How do I find the nth multiple of 15?
To find the nth multiple of 15, simply multiply 15 by n. For example, the 7th multiple of 15 is 15 × 7 = 105.
3. How can I quickly check if a number is a multiple of 15?
A number is a multiple of 15 if it's divisible by both 3 and 5. Check for divisibility by 3 (sum of digits divisible by 3) and divisibility by 5 (ends in 0 or 5). If both conditions are true, the number is a multiple of 15.
4. What is the difference between factors and multiples of 15?
Factors of 15 are numbers that divide 15 without leaving a remainder (1, 3, 5, and 15). Multiples of 15 are numbers obtained by multiplying 15 by any whole number (15, 30, 45, and so on).
5. Are all multiples of 15 also multiples of 5?
Yes, since 15 is a multiple of 5 (15 = 3 × 5), all multiples of 15 are also multiples of 5.
6. Are all multiples of 5 also multiples of 15?
No. Only multiples of 15 that are also multiples of 5 (which are all of them) are multiples of 15. For example, 25 is a multiple of 5 but not a multiple of 15.
7. What are the first five even multiples of 15?
The first five even multiples of 15 are 30, 60, 90, 120, and 150. Notice that even multiples of 15 are found by multiplying 15 by even numbers.
8. What is the least common multiple (LCM) of 15 and 10?
The LCM of 15 and 10 is 30. This is the smallest number that is a multiple of both 15 and 10.
9. Is 225 a multiple of 15? How can you tell?
Yes, 225 is a multiple of 15. You can tell because 225 ÷ 15 = 15, meaning 15 divides 225 without a remainder. Alternatively, the sum of the digits of 225 (2 + 2 + 5 = 9) is divisible by 3, and 225 ends in 5, satisfying the divisibility rules for both 3 and 5.
10. List the multiples of 15 between 100 and 200.
The multiples of 15 between 100 and 200 are: 105, 120, 135, 150, 165, 180, 195.
11. Explain the pattern in the multiples of 15.
The multiples of 15 increase by 15 each time. They alternate between odd and even numbers, and always end in either a 0 or a 5.
12. How are multiples of 15 used in real-world problems?
Multiples of 15 are useful in various real-world scenarios, such as calculating costs (e.g., items priced at $15 each), measuring lengths (e.g., 15 cm increments), or scheduling events (e.g., events occurring every 15 minutes).
