Multiples of 15 Explained with Patterns and Examples

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:

1. Check if the number is divisible by 5 (number ends in 0 or 5).
2. 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?

1. It ends with 0 ➔ divisible by 5.
2. 9+0=9 ➔ 9 is divisible by 3.
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

• Multiples of 9
• Multiples of 12
• Factors of 15
• LCM