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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. In this article, we will learn about multiples, list of some common multiples, method to find multiple of a number along with some solved examples.
Table of Content What are Multiples?Multiples are numbers obtained by multiplying one integer by another whole number. In simpler terms, a multiple of a number is the product of that number and an integer. 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 Definition
In simple terms, multiples are similar to the “skiping numbers” that result from adding the same number again. Multiples of a NumberMultiples 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 MultiplesMultiplying 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. 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 2Multiples 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 4Multiples 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 5Multiples 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.
Factors and MultiplesFactors 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. Common MultiplesCommon 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.
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 MultiplesUnderstanding the characteristics of multiples is essential in mathematics. Here are a few essential properties of multiples:
Understanding these features allows us to deal with multiples more effectively and solve a variety of mathematical problems. Read More, Solved Examples on MultiplesExample 1: List the first five multiples of 15. Solution:
Example 2: Make a list of all the factors and multiples of 10. Solution:
Example 3: Find the common multiples of 5 and 15? Solution:
Example 4: Write all the multiples of 15 between 1 and 100? Solution:
Practice Questions on MultiplesQuestion 1: Write down the first 12 multiples of 24. Question 2: How many multiples of 13 are there in between 1 and 200? Question 3: Ali sets aside 8 coins every week. How much will he have saved after 12 weeks? Question 4: Find the first three multiples of 6? Question 5: Find the common multiples of 4 and 6? Multiples: FAQsWhat are multiples?
What are common multiples?
How can we find common multiples?
Why are factors and multiples connected?
How many Multiples does a Number Have?
What is difference between multiples and factors?
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Reffered: https://www.geeksforgeeks.org
| Mathematics |
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Category: | Coding |
Sub Category: | Tutorial |
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