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Multiples of 21

Multiple of any number "n" can be obtained by the "n" times table. The multiples of 21 can be obtained by the table of 21. In this mini-lesson, we will calculate the multiples of 21, and learn interesting facts about these multiples with solved examples and interactive questions.

First five multiples of 21: 21, 42, 63, 84, 105
Prime factorization of 21: 21 = 3 × 7

1.	What Are the Multiples of 21?
2.	First 20 Multiples of 21
3.	Important Notes
4.	Tips and Tricks
5.	FAQs on Multiples of 21

What Are the Multiples of 21?

Multiples of 21 are the products when an integer is multiplied by 21. For getting the multiples of 21, we need to multiply 21 by 1, 2, 3, 4, and so on.

21 × 1 = 21
21 × 2 = 42
21 × 3 = 63
21 × 4 = 84
21 × 5 = 105

There are infinite multiples of 21. The multiples of 21 can be obtained by skip counting. Let's see how.

Multiples of 21 by Skip Counting

The multiples of 21 are either odd numbers or even numbers. The odd multiples of 21 are 21, 63, 105, and so on. 42, 82, and so on are the even multiples of 21. Both the odd multiples and the even multiples are divisible by 21.

List of First 20 Multiples of 21

Let us look at the table below showing the first 20 multiples of 21.

Multiples of 21

21 × 1 = 21
21 × 2 = 42
21 × 3 = 63
21 × 4 = 84
21 × 5 = 105
21 × 6 = 126
21 × 7 = 147
21 × 8 = 168
21 × 9 = 189
21 × 10 = 210
21 × 11 = 231
21 × 12 = 252
21 × 13 = 273
21 × 14 = 294
21 × 15 = 315
21 × 16 = 336
21 × 17 = 357
21 × 18 = 378
21 × 19 = 399
21 × 20 = 420

Did you notice 42, 84, 126, and 168 are also the multiples of 42?

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

Multiples of 12 - The first five multiples of 12 are 12, 24, 36, 48, and 60.
Multiples of 18 - The first five multiples of 18 are 18, 36, 54, 72, and 90.
Multiples of 30 - The first five multiples of 30 are 30, 60, 90,120, and 150.
Multiples of 6 - The first five multiples of 6 are 6, 12, 18, 24, and 30.
Multiples of 7 - The first five multiples of 7 are 7, 14, 21, 28, and 35.

Important Notes:

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

Tips and Tricks:

Skip counting by 21 makes it easy to find multiples of 21.
Memorize the table of 21 to list the multiples of 21 quickly.

Example 1: Help Linda find which among the first ten multiples of 21 are also the multiples of 3 and 7.

Solution:

The first 10 multiples of 21 are, 21, 42, 63, 84, 105, 126, 147, 168, 189 and 210.
Each multiple of 21 is entirely divisible by 7 and occurs in the table of 7, hence, each multiple of 21 is also the multiple of 7. As each multiple of 21 is entirely divisible by 3 and also occurs in the table of 3, hence every multiple of 21 is also a multiple of 3.

We conclude that all the first ten multiples of 21 are also the multiples of 3 and 7.
Example 2: Pick all the odd multiples of 21 from the given list.

21, 42, 63, 84, 126, 147, 189, 210

Solution:

Odd numbers are those which are not divisible by 2. The odd multiples in the list are 21, 63, 147, and 189.
Hence, Odd multiples of 21 = 21, 63, 147, 189

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FAQs on Multiples of 21

How many multiples does 21 have?

The number of multiples of any number is infinite. For example, multiples of 21 are 21, 42, 63, and so on.

Are the multiples of 21 always odd? Explain.

No, the multiples of 21 are not always odd. When 21 is multiplied by an even number the product is an even number while on multiplication of 21 by an odd number the product is an odd number.

What is the sum of the first five multiples of 21?

First five multiples of 21 are, 21, 42, 63, 84, and 105.
The sum of first five multiples of 21 is 315.

What is the least common multiple of 21 and 14?

The least common multiple of two numbers 21 and 14 is calculated by the formula: (21 × 14)/GCF(21, 14).
Here GCF(21, 14) is the greatest common factor of 21 and 14.

GCF(21, 14) = 7
LCM(21, 14) = (21 × 14)/GCF(21, 14) = 21 × 2 = 42

Can there be negative multiples of 21?

Yes, there can be negative multiples of 21.

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