# Multiples of 12

Have you noticed that the number 12 is one of the useful numbers that we encounter almost every day?

When you wake up in the morning, you tend to check what time it is already, and you see that your clock displays 12 dials. You might also think of the date today and realize we have 12 months in a year.

Going to the market, you might ask a vendor to give you a dozen of oranges and two dozens of eggs, thinking that “dozen” means a group or a set of 12.

You might also measure something where you observe that a yard is made up of 12 feet, and a foot is made up of 12 inches.

You might be surprised, but the number 12 is also present in our bodies. The human body has 12 pairs of cranial nerves and an average of 12 pairs of ribs. Additionally, the weight of our blood is about 1/12 of the weight of our body.

With all of that being said, isn’t it interesting to explore another world of multiples, the multiples of 12? Learning such will aid us in making our calculations simpler and easier!

Are you looking forward to our next learning quest about multiples of 12? Hold on tight, because we’re about to embark on yet another meaningful mathematical journey!

## Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 …

We have learned that multiples are the numbers we get when we multiply a number by another number.

So, the multiples of 12 are the result when we multiply 12 by another integer, such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on.

Notice that the consecutive multiples of 12 produce a number sequence wherein the difference of two consecutive numbers is 12. Each number in the sequence will result in a whole number when divided by 12.

For example, 156 is a multiple of 12 because it is the product of 12 and 13.

In other words, a multiple of 12 is the product of 12 and any integer. So, it would be best to keep in mind that fractions must not be used to find multiples.

Wow! Isn’t that simple?

Now, let us continue our learning journey on how to find any multiples of 12!

## How to find the multiples of 12?

Suppose $$n$$ is a counting number. To get the *$$n^{th}$$* multiple of 12, we must multiply 12 by $$n$$ or add 12 $$n$$ times.

For example, if we want to determine the third multiple of 12, we must multiply 12 by 3, $$12\times3 = 36$$. We can also do repeated addition of 12, that is, 12 + 12 + 12 = 36. Hence, the third multiple of 12 is 36.

Let’s observe the figure below and see how simple it is to find multiples of 12 by repeated addition.

Isn’t that easy? Now, let us try another example by finding the sixth multiple of 12.

By multiplication, the sixth multiple of 12 can be expressed as $$12 \times 6$$ and by repeated addition as 12 + 12 + 12 + 12 + 12 + 12. Both methods resulted in 72. Thus, the sixth multiple of 12 is 72.

Now, you can efficiently find any number that is a multiple of 12!

## List of the First 30 multiples of 12

We have known that we have infinitely many numbers, and so do the multiples of 12. Below is the list of the first 30 multiples of 12, obtained by multiplying 12 by the integers from 1 to 30.

Product of 12 and a positive counting number | Multiples of 12 |
---|---|

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 |

12 × 21 | 252 |

12 × 22 | 264 |

12 × 23 | 276 |

12 × 24 | 288 |

12 × 25 | 300 |

12 × 26 | 312 |

12 × 27 | 324 |

12 × 28 | 336 |

12 × 29 | 348 |

12 × 30 | 360 |

Has it occurred to you that the multiples of the number 12 in the table above correspond to the results in the multiplication table of 12? Right! Because both tables are the same.

We can also find the multiples of 12 by adding it repeatedly. All we have to do is to add 12 as many times as required. For example, the first five multiples of 12 are listed in the table below.

n^{th }multiple of 12 |
by Multiplication | by Repeated Addition | Multiples of 12 |
---|---|---|---|

1 |
12 × 1 |
12 |
12 |

2 |
12 × 2 |
12 + 12 |
24 |

3 |
12 × 3 |
12 + 12 + 12 |
36 |

4 |
12 × 4 |
12 + 12 + 12 + 12 |
48 |

5 |
12 × 5 |
12 + 12 + 12 + 12 + 12 |
60 |

## Did you know that…

The sundial was invented by the Egyptians as early as 1500 B.C. The sundial was calibrated to divide the time period between sunrise and sunset into 12 equal parts. Such a system reflects the fact that they use a base 12 number system or a duodecimal system.

This system can be attributed to either the 12 lunar cycles of the year or to the number of finger joints on each hand (3 on each of the 4 fingers excluding the thumb), which the Egyptians in counting to 12.

You can easily count the three segments on each finger to make 12 using the thumb as a pointer. Both hands will make you count up to 24.

Isn’t it amazing how Egyptians made such a significant contribution that we still benefit from today?

## Problems involving multiples of 12

Now, let us apply what we have learned about multiples of 12 in solving real-life problems!

### Problem #1

Susan sells fruit per dozen. If she has sold five dozens of apples, six dozens of oranges, and a dozen of watermelon in a day, how many pieces of fruits did she sell in all that day?

To solve this, we must add the number of dozens that Susan sold first. So,** 5 + 6 + 1 = 12**. Hence, Susan sold **12 dozens** of fruits.

Now, since we know that a dozen means a set of 12, we must find the 12th multiple of 12 to determine the total number of fruits she sold. To do this, we simply multiply 12 by 12. Thus, $$12 \times 12 = 144$$.

Therefore, Susan sold a total of **144 fruits**.

Did you get the same answer? Now let us try to solve another problem.

### Problem #2

Marcus work on a project for 12 hours a day. If he finished the project in 6 days, how much did Marcus earn if he was paid $3 for every hour he worked?

To answer this, we must find the 6^{th} multiple of 12 to determine Marcus’s total number of hours to finish the project. So, $$12\times6 = 72$$. Thus, he finished the project in **72 hours**.

Next, we must multiply 72 by 3 to compute for his total earnings from the project. Hence, $$72\times 3 = 216$$.

Therefore, Marcus earned **$216** after finishing the project.

Great! I bet you now agree that learning about the multiples of 12 is helpful in solving real-life problems.

## Take a quiz

Now that you understand and learn the concept of multiples of 12, it’s time for you to take a challenge by answering the following questions.