# Multiples of 12

## 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.

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 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 stands of 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.

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

Ans: 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 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. Demonstrate the Actual Difference Between Factors and Multiples.

Ans: 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.