Multiples of 12 - Methods of Finding Multiples

Dhristi JEE 2022-24

What are Multiples and What are the Multiples of 12?

Before knowing the multiples of 12, let us first look into the concept of multiples. A multiple of a number is the result of the product of that number with any other number. Multiples are usually considered in the form of whole numbers. In other words, the number that can be divided by another number completely without leaving a remainder is called the multiple of that number. In this article, we will learn about all multiples of 12. Thus, the numbers that we will be focusing on are completely divisible by 12. 

 

People often tend to get confused when they come across terms like multiples and factors. There is a thin line that differentiates both. The numbers that can completely divide a number without leaving a remainder are called the factors of that number. The basic concept is that 12 is the factor of the multiples of 12. 

 

Multiple is a number which is always reached by multiplying a given number by another. While factors of a number are finite, multiples always have to be infinite in number. Factors are what can be multiplied with another number to get the required number. There is a minimum of two factors for every number, i.e. 1 and the number itself. 

 

There is no end to the multiples of a specific given number. For finding out the multiples of a given number, we have to multiply that particular number by integers beginning with number1. The resultant number after the multiplication of the given numbers, is the multiple of the more existing  given number.

 

Properties of a Multiple

Any number that is a multiple of 2 is an even number

e.g., 2, 4, 6, 8, 10…. Etc

 

All the non 2 multiple numbers are called odd numbers 

e.g., 1, 3, 7, 9, 11, 13….. Etc

 

There are an infinite number of multiples. There can be no limit to it.

 

Every integer is multiple in itself.

 

The smallest multiple is the number itself.

 

A product is always the multiple of all its factors. 

 

0 is a multiple of any number. 

 

Methods of Finding out Multiples

Least Common Multiple -

  1. Listing Method

In the listing method, we find the least common multiple which exists as the listing of all the numbers.

  1. Tree Factor

The tree factor, the factor tree, or prime factorization. It is a useful way of finding a factor of any integer till we have reached the prime number and we cannot factor anymore. Finding the least common multiple through the tree factor method is a more fun way of breaking down a large number and building it back up. Through the tree factor method, we can conduct a prime factorization of any two or more numbers. It is a useful tool for breaking down large and more difficult problems.

  1. Ladder Method

The ladder/grid is a method of finding out the least common multiple of two or more numbers. We can find the LCM of larger numbers in a much faster way. The ladder or grid closely looks like a tic tac toe grid. It is a set of two horizontal parallel lines that go around to intersect each other at a very vertical angle.

  1. LCM Of Mixed Fractions

The best way to find a common denominator of a proper or improper fraction has to be the LCM method in the case of the mixed fractions. In this method, we use the ladder LCM method for both the denominator number of the fraction to come up with a more common number.


Grid Method Multiplication

The grid method is also known as the grammar school or the box method. It is a good place to begin learning multiple numbers and the calculations with larger numbers that are more than number 10.


For example, 5 is a factor of 35, i.e. 5 completely divides 35 without leaving a remainder and having a quotient of 7. Conversely, 7 is also a factor of 35 as it gives 5 as a quotient on division. Thus 35 has factor-like 5, 7, 35, and 1 which divide 35 without any remainder.

 

On the other hand, 35 is a multiple of 5 as well as a multiple of 7.

                           5             x            7               =            35 

                factor of 35            factor of 35         multiple of 5 or 7

 

12 Multiples

A multiple of 12 is a number that can be represented in the form of 12n, where any natural number. A number that can be divided a certain number of times by another number is called the multiple of the other number. Suppose we have two numbers A and B.

 

A is said to be the multiple of B if, A = nB, where n stands for natural numbers. The basic difference between factors and multiples are:

Multiples

Factors

All multiples can be interpreted as the numbers obtained as a result when multiplied by other numbers

Factors are elucidated as the precise divisors of the given number

There are an infinite number of multiples

There are finite numbers of factors for each number.

The operation of multiplication is used to find the multiple of a number.

The operation of division is used to find the factors of a number.

The product of the multiples should be greater than or equal to the given number

Factors of a number should be less than or equal to the given number

 

Common 5 Multiples of 12 are:

24, 36, 60, 120, 144 etc.

 

The numbers that are products of 12 or can be divided by 12 without leaving a remainder are multiples of 12. As per the construction of the equation, it is easy to identify the multiples as well as factors of a given number. For example, 24, 36, 60, 120, and 144 are all common multiples of 12 pertaining to the following arrangement of equations:

 

Factors

Multiples of 12

12 x 2 =

24

12 x 3 =

36

12 x 5 =

60

12 x 10 =

120

12 x 12 =

144

 

These are all represented as multiples as they are procured by adding or subtracting the original number i.e. 12, multiple times.

 

The different important multiples of 12 are:

Product

Multiples

12 × 1 =

12

12 × 2 =

24

12 × 3 =

36

12 × 4 =

48

12 × 5 =

60

12 × 6 =

72

12 × 7 =

84

12 × 8 =

96

12 × 9 =

108

12 × 10 =

120

12 × 11 =

132

12 × 12 =

144

12 × 13 =

156

12 × 14 =

168

12 × 15 =

180

12 × 16 =

192

12 × 17 =

204

12 × 18 =

216

12 × 19 =

228

12 × 20 =

240

 

Least Common Multiple of 12

The Least Common Multiple is also referred to as Lowest Common Multiple or Least Common Divisor. If there are two integers a and b, in that case, the smallest positive integer that is evenly divisible by both a and b is the least common multiple of a and b.


Suppose there are two numbers 12 and 6, the LCM (12,6) = 12

 

Did You Know?

The LCM of two or more numbers is the smallest number that is divisible by the whole set of numbers without leaving a remainder.

 

Just like the multiples of 12 are 12, 36, 48, 60, 72, 84, 96, and so on, on the contrary 1,2,3,4,6 and 12 are factors of 12.

 

Conclusion

This is how we can calculate the multiples of 12 and learn how to calculate the same for other numbers. Just follow the process and understand how we can utilize the same concept to solve problems in no time. 

FAQs on Multiples of 12 - Methods of Finding Multiples

1. Mention Some of the Multiples of 12 within 1000.

There are many multiples of 12 between 1 and 1000. Precisely, there are 83 multiples of 12 within 1000. Some of the common multiples of 12, first, within the first 100 are 12, 24, 96, 204, 336, 444, 540, 672, 768, 804, 888, 972, and 984. The last multiple of 12 before 1000 is 996.  The factors of 12, on the other hand, as we all know are 12 and 1, 2 and 6, and 3 and 4. It is very important for every student to keep in mind the major multiples of 12, at least within 100, for easy calculation. It helps save time and fetches good marks in the examination as well. 

2. What are the properties of a multiple?

0 is a multiple of every number.


The product of any integer is n and any integer has to be a multiple of n. In particular n, it is equal to n*1  is a multiple of n  because every integer is a multiple of also itself), since 1 is an integer. 


If a and b are multiples of x, then a + b, a - b are also multiples of x.

3. Demonstrate the Actual Difference Between Factors and Multiples.

The actual difference between factors and multiples is that a number is a factor of its own multiple. Here multiple of a number is the product of that number with any other number. Thus, it can be concluded that when M and N are two numbers:

  • If M divides N, we can say that M is a factor of N

  • If N is divisible by M is obvious that N is a multiple of M

Every number is divisible by 1 without leaving a remainder. Thus, 1 is the lowest common factor of all numbers. Speaking of multiples, when all numbers are divisible by 1, that suggests that all numbers can be considered as multiple of 1.

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