Multiples of 3 – 100+ List, Examples

Multiples of 3 are integers that can be obtained by multiplying the number 3 by any whole number. These numbers, such as 3, 6, 9, 12, and so on, are the result of the multiplication process involving 3. The concept of multiples is closely related to factors and divisors; specifically, a multiple of 3 is any number that 3 can evenly divide without leaving a remainder. Understanding multiples helps in various mathematical applications, including finding common multiples and solving problems involving divisibility.

For example, 70, 80, 20 and 60 are all multiples of 3, 22 is not a multiple of 3 for the following reasons:

List of First 100 Multiples of 3 with Remainders

Read More About Multiples of 3

Table of 3

Important Notes

• Definition: Multiples of a number are obtained by multiplying the number by integers (e.g., multiples of 2 are 2, 4, 6, 8, …).
• Divisibility: A number is a multiple of another if it can be divided by that number without leaving a remainder.
• Sequence: The sequence of multiples is infinite. For instance, multiples of 2 are 2, 4, 6, 8, 10, and so on, continuing indefinitely.
• Applications: Understanding multiples is crucial for solving problems in arithmetic, algebra, and number theory, such as finding the least common multiple (LCM) and greatest common divisor (GCD).
• Pattern Recognition: Recognizing patterns in multiples helps in simplifying calculations and solving mathematical puzzles and problems effectively.

Examples on Multiples of 3

Example 1: Checking if a Number is a Multiple of 3

To determine if 45 is a multiple of 3, divide 45 by 3: 45÷3 = 15 Since the result is an integer with no remainder, 45 is a multiple of 3.

Example 2: Finding Multiples of 3

To find the first five multiples of 3, multiply 3 by the first five integers:

• 3×1 = 3
• 3×2 = 6
• 3×3 = 9
• 3×4 = 12
• 3×5 = 15

Thus, the first five multiples of 3 are 3, 6, 9, 12, and 15.

Example 3: Real-Life Application

Consider you have 27 apples, and you want to distribute them equally into groups of 3: 27÷3 = 9 You will have 9 groups with 3 apples each. This shows that 27 is a multiple of 3.

Example 4: Summing Multiples of 3

Find the sum of the multiples of 3 up to 15:

• Multiples: 3, 6, 9, 12, 15
• Sum: 3+6+9+12+15 = 45

Therefore, the sum of the multiples of 3 up to 15 is 45.

Example 5: Multiples of 3 within a Range

Identify multiples of 3 between 10 and 30:

• Starting from 12 (the first multiple of 3 greater than 10)
• 12, 15, 18, 21, 24, 27, 30

Practical Examples of Multiples of 3

Example 1: Sharing Candies

You have 18 candies and want to divide them equally among 3 friends. Each friend gets: 18÷3 = 6 So, 18 is a multiple of 3.

Example 2: Counting Steps

If you take 3 steps at a time, after 5 times, you will have taken: 3×5 = 15 Therefore, 15 steps is a multiple of 3.

Example 3: Packing Items

You have 27 books to pack into boxes, with 3 books per box. You will need: 27÷3 = 9 This means 27 is a multiple of 3, requiring 9 boxes.

Example 4: Buying Tickets

Concert tickets are sold in packs of 3. If you need 12 tickets, you will buy: 3×4 = 12 So, 12 is a multiple of 3, and you buy 4 packs.

Example 5: Arranging Chairs

You want to arrange 30 chairs in rows of 3. The number of rows will be: 30÷3 = 10 Thus, 30 is a multiple of 3, and you will have 10 rows.

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