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Multiples of 3

Did you know the term "multiples" has a Latin origin and comes from the word "multiplex," where "multi" means "many," and "plex" means "fold?" Knowing the multiples of a number makes our calculations faster and easier. In this mini-lesson, we will calculate the multiples of 3 and learn interesting facts about these multiples.

First five multiples of 3: 3, 6, 9, 12, 15
Prime factorization of 3: 3 = 3¹

1.	What Are the Multiples of 3?
2.	First 20 Multiples of 3
3.	Important Notes
4.	FAQs on Multiples of 3
5.	Tips and Tricks

What Are the Multiples of 3?

A multiple is a result of multiplying a number by an integer. Multiples of 3 are the products obtained when an integer is multiplied by 3.

For getting the multiples of 3, we need to multiply 3 by 1, 2, 3, 4, and so on.

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

As we list them down, we see that there are infinite multiples of 3. Observe the multiples of 3 represented on a number line.

Representation of Multiples of 3 on a Number Line

The multiples of 3 can be odd numbers or even numbers. The odd multiples of 3 are 3, 9, 15, and so on, which are not divisible by 2, whereas, 6, 12, 18, and so on are the even multiples of 3, which are divisible by 2.

List of First 20 Multiples of 3

Let us write down the first 20 multiples of 3.

Multiplying 3 by integers

3 × 1 = 3
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12
3 × 5 = 15
3 × 6 = 18
3 × 7 = 21
3 × 8 = 24
3 × 9 = 27
3 × 10 = 30
3 × 11 = 33
3 × 12 = 36
3 × 13 = 39
3 × 14 = 42
3 × 15 = 45
3 × 16 = 48
3 × 17 = 51
3 × 18 = 54
3 × 19 = 57
3 × 20 = 60

Did you observe that 15, 30, 45, and 60 are also the multiples of 5?

To understand the concept of finding multiples, let us take a few more examples.

Multiples of 30 - The first five multiples of 30 are 30, 60, 90, 120, 150
Multiples of 36 - The first five multiples of 36 are 36, 72, 108, 144, 180
Multiples of 13 - The first five multiples of 13 are 13, 26, 39, 52, 65
Multiples of 7 - The first five multiples of 7 are 7, 14, 21, 28, 35
Multiples of 63 - The first five multiples of 63 are 63, 126, 189, 252, 315

Important Notes:

Multiples are what we get after multiplying two numbers.
The number of multiples for a given number are infinite.
Every number is a multiple of itself.
A multiple of the given number is always equal to or greater than the number.

Tips and Tricks:

Skip counting by 3 helps to find multiples of 3.
Memorize the table of 3 to list the multiples of 3.

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Example 1: Tom's teacher told him to find the first 3 multiples of 5. Can you help Tom in this work?

Solution:

Let us multiply 5 with the first 3 numbers 1, 2, and 3.
- 5 × 1 = 5
- 5 × 2 = 10
- 5 × 3 = 15
Hence, the first 3 multiples of 5 are 5, 10, and 15.
Example 2: Pick all the odd multiples of 3 from the given list.

3, 6, 9, 12, 15, 18, 21, 27

Solution:

Odd numbers are those which are not divisible by 2. The odd multiples in the list are 3, 9, 15, 21, 27.
Hence, odd multiples of 3 = 3, 9, 15, 21, 27
Example 3: Monica is given a list of numbers divided into 4 groups. She needs to select the group which only has multiples of 2. Can you name the group?

Group A: 2, 3, 4

Group B: 2, 4, 6

Group C: 1, 2, 3

Group D: 3, 5, 7

Solution:

Group A has 2 even numbers and one odd number. Group B has only even numbers. Group C has 2 odd numbers and one even number.
Group D has only odd numbers.

Hence, the answer is Group B since all even numbers are the multiples of 2.

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FAQs on Multiples of 3

How many multiples does 3 have?

The number of multiples of any number is infinite. eg: 3, 6, 9, 12, 15, 18, etc.

Are the multiples of 3 always odd? Explain.

No, the multiples of 3 are not always odd. For example 6, 12, and 18 are even numbers and are multiples of 3. When 3 is multiplied by an even number, the product will be an even number. When 3 is multiplied by an odd number, the product will be an odd number.

What is the sum of first five multiples of 3?

The first five multiples of 3 are 3, 6, 9, 12, and 15.
The sum of first five multiples of 3 is 3 + 6 + 9 + 12 + 15 = 45

Hence, the sum of first five multiples of 3 is 45.

What is the least common multiple of 3 and 9?

The least common multiple of two numbers can be calculated using the formula: product of the numbers/GCF of the numbers. Here GCF(3,9) is the greatest common factors of 3 and 9.

GCF (3, 9) = 3
LCM (3, 9) = (3 × 9)/GCF(3, 9) = 27/3 = 9

What are the first five multiples of 3?

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

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