Multiples

Multiples, in mathematics, are the numbers obtained by the product of the original number with another integer like 1, 2, 3, etc. Every number has infinite multiples. For example, 30 is a multiple of 5 as 5 × 6 = 30.

Let us take a number, say 7. If we begin multiplying 7 by various whole numbers, we will receive a sequence of multiples. For example, multiplying 7 by 1 yields 7. That is the first multiple of 7. Then, multiplying 7 by 2 yields 14, So 14 is another multiple of 7. Continuing the same way we can get other multiples of 7 like 21, 28, 35, etc.

Multiples of a Number

Multiples of a number are a sequence of numbers formed by adding the same number repeatedly or multiplying it by various whole numbers. For example, the number 6 has multiples 6, 12, 18, etc. Each of these numbers is the result of multiplying 6 by 1, 2, 3, etc.

Multiples help us grasp how numbers develop and may be beneficial in a variety of circumstances, including pattern recognition and arithmetic problem solving.

List of Multiples

Multiplying an integer with natural numbers yields its multiples. As there are infinitely many natural numbers, there are infinitely many multiples of any given integer. The list of multiples of a number is endless.

For example, multiplying a number by 1, 2, 3, and so on yields its multiples. The table below shows the first ten multiples of particular numbers. Remember that we may continue to discover multiples by multiplying the number by larger natural integers.

Understanding multiples allows us to comprehend how numbers expand and see patterns in their sequences.

Factors and Multiples

Factors and multiples are two closely connected topics in mathematics. The explanation of these terms are given below:

Factor is a number that divides another number evenly and produces no residue. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, as each of these numbers divides 12 without leaving any remainder.

On the other hand, a multiple of a number is the result of multiplying one integer by another. For example, the multiples of number 5 are 5, 10, 15, 20, and so on, since each of these numbers is the result of multiplying 5 by 1, 2, 3, 4, and so on.

Hence, factors split a number evenly and multiples are the results of multiplication with another number.

Also read : Greatest Common Divisor ( GCD )

Common Multiples

Common multiple are the multiples which are common in two or more numbers. In other words, common multiple are numbers that appear in a list of multiples for two or more distinct numbers.

Let's take an example of the multiples of 2 and 3.

• Multiples of 2 are 2, 4, 6, 8, 10, 12, and so on.
• Multiples of 3 are 3, 6, 9, 12, 15, 18, and so on.

When we compare both lists, we can observe that the number 6 appears on both. So 6 is the first common multiple of 2 and 3.

Properties of Multiples

Understanding the characteristics of multiples is essential in mathematics. Here are a few essential properties of multiples:

• Every multiple of a number is equal to or greater than the original number. For example, multiples of three include 3, 6, 9, 12, and so on, all of which are equal to or larger than 3.

• Number of multiples of any given integer are infinite. For example, the multiples of 4 are 4, 8, 12, 16, and so on, and the list could go on forever.

• Each number is a multiple of itself. .

• Every number is a multiple of 1, and 0 is a multiple of every integer.

Understanding these features allows us to deal with multiples more effectively and solve a variety of mathematical problems.

How to Find Multiples of a Number?

To find multiples of a number, we simply multiply the given number by another whole number. For example, if we have a number 3, its multiples are numbers like 3, 6, 9, 12, and so on, which are obtained by multiplying 3 by 1, 2, 3, 4, and so on.

We can also find multiples of a number by continuously adding the given integer to itself. For example, to find multiples of 10, we add 10 to to itself several times and obtained multiples are: 10, 20, 30, 40......

Let us look at the multiples of some common numbers:

Multiples of 2

Multiples of 2 are numbers obtained by multiplying two by whole numbers such as 1, 2, 3, etc. Another method for finding multiples of 2 is to add 2 to itself repeatedly.

Let's use these methods to look at the first ten multiples of two.

Multiples of 4

Multiples of 4 are numbers obtained by multiplying 4 by integers such as 1, 2, 3, and so on. Alternatively, we may generate multiples of 4 by repeatedly adding 4 to itself.

Let's look at the first ten multiples of four.

Multiples of 5

Multiples of 5 are the numbers obtained by multiplying 5 by whole numbers such as 1, 2, 3, and so on. We may also discover multiples of 5 by adding 5 repeatedly.

Let's use these methods to look at the first ten multiples of five.

Read More,

• Number System
• Number
• Integers

Solved Examples on Multiples

Example 1: List the first five multiples of 15.
Solution:

To find the first five multiples of 15, multiply 15 by the first five natural integers.

15 × 1 = 15
15 × 2 = 30
15 × 3 = 45
15 × 4 = 60
15 × 5 = 75

∴ The first five multiples of 15 include 15, 30, 45, 60 and 75.

Example 2: Make a list of all the factors and multiples of 10.
Solution:

The factors of 10 are 1, 2, 5 and 10.
The multiples of 10 include 10, 20, 30, 40, 50, 60 and so on.

Example 3: Find the common multiples of 5 and 15?
Solution:

Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, . . . . . . .
Multiple of 15 are: 15, 30, 45, 60, 75, 90, 105, . . . . . . .

Common multiples of 5 and 15 are: 15, 45, . . . . . . .

Example 4: Write all the multiples of 15 between 1 and 100?
Solution:

Multiples of 15 between 1 and 100 are: 15, 30, 45, 60, 75 and 90.