## Multiples of 12

In mathematics, multiples of 12 are numbers that result from multiplying 12 by any integer. These multiples form an important concept as they help in understanding various topics such as multiplication, divisors, and factors. For example, the first few multiples of 12 include 12, 24, 36, and so on. Since 12 is a composite number, its multiples also reflect its divisors and factors. Understanding the multiples of 12 aids in solving problems involving numbers and their properties.

## What are Multiples of 12?

**Multiples of 12 are numbers obtained by multiplying 12 by any integer, such as 12, 24, 36, etc.** They represent the products that include 12 as one of their factors.

**Prime factorization of 12**: 2 × 2 × 3

**First 10 multiples of 12:**12, 24, 36, 48, 60, 72, 84, 96, 108, 120.

## For example, 36, 72, 96 and 120 are all multiples of 50, 150 is not a multiple of 11 for the following reasons:

Number | Reason | Remainder |
---|---|---|

36 | 36 ÷ 12 = 3 (an integer) | 0 |

72 | 72 ÷ 12 = 6 (an integer) | 0 |

96 | 96 ÷ 12 = 8 (an integer) | 0 |

120 | 120 ÷ 12 = 10 (an integer) | 0 |

150 | 150 ÷ 11 = 13.636 (not integer) | 7 |

## List of First 100 Multiples of 12 with Remainders

Number | Reason | Remainder |
---|---|---|

12 | 12 ÷ 12 = 1, which is an integer | 0 |

24 | 24 ÷ 12 = 2, which is an integer | 0 |

36 | 36 ÷ 12 = 3, which is an integer | 0 |

48 | 48 ÷ 12 = 4, which is an integer | 0 |

60 | 60 ÷ 12 = 5, which is an integer | 0 |

72 | 72 ÷ 12 = 6, which is an integer | 0 |

84 | 84 ÷ 12 = 7, which is an integer | 0 |

96 | 96 ÷ 12 = 8, which is an integer | 0 |

108 | 108 ÷ 12 = 9, which is an integer | 0 |

120 | 120 ÷ 12 = 10, which is an integer | 0 |

132 | 132 ÷ 12 = 11, which is an integer | 0 |

144 | 144 ÷ 12 = 12, which is an integer | 0 |

156 | 156 ÷ 12 = 13, which is an integer | 0 |

168 | 168 ÷ 12 = 14, which is an integer | 0 |

180 | 180 ÷ 12 = 15, which is an integer | 0 |

192 | 192 ÷ 12 = 16, which is an integer | 0 |

204 | 204 ÷ 12 = 17, which is an integer | 0 |

216 | 216 ÷ 12 = 18, which is an integer | 0 |

228 | 228 ÷ 12 = 19, which is an integer | 0 |

240 | 240 ÷ 12 = 20, which is an integer | 0 |

252 | 252 ÷ 12 = 21, which is an integer | 0 |

264 | 264 ÷ 12 = 22, which is an integer | 0 |

276 | 276 ÷ 12 = 23, which is an integer | 0 |

288 | 288 ÷ 12 = 24, which is an integer | 0 |

300 | 300 ÷ 12 = 25, which is an integer | 0 |

312 | 312 ÷ 12 = 26, which is an integer | 0 |

324 | 324 ÷ 12 = 27, which is an integer | 0 |

336 | 336 ÷ 12 = 28, which is an integer | 0 |

348 | 348 ÷ 12 = 29, which is an integer | 0 |

360 | 360 ÷ 12 = 30, which is an integer | 0 |

372 | 372 ÷ 12 = 31, which is an integer | 0 |

384 | 384 ÷ 12 = 32, which is an integer | 0 |

396 | 396 ÷ 12 = 33, which is an integer | 0 |

408 | 408 ÷ 12 = 34, which is an integer | 0 |

420 | 420 ÷ 12 = 35, which is an integer | 0 |

432 | 432 ÷ 12 = 36, which is an integer | 0 |

444 | 444 ÷ 12 = 37, which is an integer | 0 |

456 | 456 ÷ 12 = 38, which is an integer | 0 |

468 | 468 ÷ 12 = 39, which is an integer | 0 |

480 | 480 ÷ 12 = 40, which is an integer | 0 |

492 | 492 ÷ 12 = 41, which is an integer | 0 |

504 | 504 ÷ 12 = 42, which is an integer | 0 |

516 | 516 ÷ 12 = 43, which is an integer | 0 |

528 | 528 ÷ 12 = 44, which is an integer | 0 |

540 | 540 ÷ 12 = 45, which is an integer | 0 |

552 | 552 ÷ 12 = 46, which is an integer | 0 |

564 | 564 ÷ 12 = 47, which is an integer | 0 |

576 | 576 ÷ 12 = 48, which is an integer | 0 |

588 | 588 ÷ 12 = 49, which is an integer | 0 |

600 | 600 ÷ 12 = 50, which is an integer | 0 |

612 | 612 ÷ 12 = 51, which is an integer | 0 |

624 | 624 ÷ 12 = 52, which is an integer | 0 |

636 | 636 ÷ 12 = 53, which is an integer | 0 |

648 | 648 ÷ 12 = 54, which is an integer | 0 |

660 | 660 ÷ 12 = 55, which is an integer | 0 |

672 | 672 ÷ 12 = 56, which is an integer | 0 |

684 | 684 ÷ 12 = 57, which is an integer | 0 |

696 | 696 ÷ 12 = 58, which is an integer | 0 |

708 | 708 ÷ 12 = 59, which is an integer | 0 |

720 | 720 ÷ 12 = 60, which is an integer | 0 |

732 | 732 ÷ 12 = 61, which is an integer | 0 |

744 | 744 ÷ 12 = 62, which is an integer | 0 |

756 | 756 ÷ 12 = 63, which is an integer | 0 |

768 | 768 ÷ 12 = 64, which is an integer | 0 |

780 | 780 ÷ 12 = 65, which is an integer | 0 |

792 | 792 ÷ 12 = 66, which is an integer | 0 |

804 | 804 ÷ 12 = 67, which is an integer | 0 |

816 | 816 ÷ 12 = 68, which is an integer | 0 |

828 | 828 ÷ 12 = 69, which is an integer | 0 |

840 | 840 ÷ 12 = 70, which is an integer | 0 |

852 | 852 ÷ 12 = 71, which is an integer | 0 |

864 | 864 ÷ 12 = 72, which is an integer | 0 |

876 | 876 ÷ 12 = 73, which is an integer | 0 |

888 | 888 ÷ 12 = 74, which is an integer | 0 |

900 | 900 ÷ 12 = 75, which is an integer | 0 |

912 | 912 ÷ 12 = 76, which is an integer | 0 |

924 | 924 ÷ 12 = 77, which is an integer | 0 |

936 | 936 ÷ 12 = 78, which is an integer | 0 |

948 | 948 ÷ 12 = 79, which is an integer | 0 |

960 | 960 ÷ 12 = 80, which is an integer | 0 |

972 | 972 ÷ 12 = 81, which is an integer | 0 |

984 | 984 ÷ 12 = 82, which is an integer | 0 |

996 | 996 ÷ 12 = 83, which is an integer | 0 |

1008 | 1008 ÷ 12 = 84, which is an integer | 0 |

1020 | 1020 ÷ 12 = 85, which is an integer | 0 |

1032 | 1032 ÷ 12 = 86, which is an integer | 0 |

1044 | 1044 ÷ 12 = 87, which is an integer | 0 |

1056 | 1056 ÷ 12 = 88, which is an integer | 0 |

1068 | 1068 ÷ 12 = 89, which is an integer | 0 |

1080 | 1080 ÷ 12 = 90, which is an integer | 0 |

1092 | 1092 ÷ 12 = 91, which is an integer | 0 |

1104 | 1104 ÷ 12 = 92, which is an integer | 0 |

1116 | 1116 ÷ 12 = 93, which is an integer | 0 |

1128 | 1128 ÷ 12 = 94, which is an integer | 0 |

1140 | 1140 ÷ 12 = 95, which is an integer | 0 |

1152 | 1152 ÷ 12 = 96, which is an integer | 0 |

1164 | 1164 ÷ 12 = 97, which is an integer | 0 |

1176 | 1176 ÷ 12 = 98, which is an integer | 0 |

1188 | 1188 ÷ 12 = 99, which is an integer | 0 |

1200 | 1200 ÷ 12 = 100, which is an integer | 0 |

## Read More About Multiples of 12

## Important Notes

### Definition and Basic Concept

**Definition**: A multiple of 12 is any number that can be expressed as 12×n where n is an integer.**Basic Concept**: Multiples of 12 are found by multiplying 12 by whole numbers (both positive and negative, including zero).

### First Few Multiples of 12

The initial multiples of 12 are:

- 12×1 = 12
- 12×2 = 24
- 12×3 = 36
- 12×4 = 48
- 12×5 = 60

### Properties of Multiples of 12

**Divisibility**: A number is a multiple of 12 if it is divisible by both 3 and 4.- To check divisibility by 3: The sum of the digits of the number must be divisible by 3.
- To check divisibility by 4: The last two digits of the number must be divisible by 4.

**Even Number**: All multiples of 12 are even because 12 itself is even.

**Common Multiples**: Multiples of 12 are also multiples of its factors: 1, 2, 3, 4, and 6.

### Finding Multiples of 12

**Formula**: To find the n-th multiple of 12, use the formula 12×n.**Example Calculation**: For n = 8, the multiple of 12 is 12×8 = 96.

### Real-World Applications of Multiples of 12

**Time**: There are 12 hours on a clock face, and multiples of 12 are significant in measuring time (e.g., 24 hours in a day).**Packaging**: Items are often packaged in dozens (12 items) or gross (144 items, which is 12×12).**Calendars**: There are 12 months in a year.

### Summary Table of Multiples of 12

Multiple | Value |
---|---|

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 |

## Examples on Multiples of 12

### Multiples of 12 from 1 to 10

Multiples of 12 are obtained by multiplying 12 with different whole numbers. Here are the first 10 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

### Common Multiples of 12 and 8

To find common multiples, list the multiples of each number and find the overlap.

**Multiples of 12:** 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, …

**Multiples of 8:** 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, …

**Common Multiples:** 24, 48, 72, 96, 120, …

### Real-World Example: Packaging

Suppose you have a factory that produces boxes of 12 bottles each. If you need to ship 5 boxes, you can calculate the total number of bottles as follows:

- 12 bottles/box × 5 boxes = 60 bottles

## FAQs

## What are multiples of 12?

Multiples of 12 are numbers that can be expressed as 12 multiplied by an integer. Examples include 12, 24, 36, 48, and so on.

## How can I find the first five multiples of 12?

To find the first five multiples of 12, multiply 12 by the first five positive integers:

12 × 1 = 12

12 × 2 = 24

12 × 3 = 36

12 × 4 = 48

12 × 5 = 60

**Are all multiples of 12 also multiples of 3 and 4?**

Yes, since 12 is a multiple of both 3 and 4, all multiples of 12 are also multiples of 3 and 4. For example, 24 is a multiple of 12, 3, and 4.

## What is the least common multiple (LCM) of 12 and another number?

The LCM of 12 and another number is the smallest number that is a multiple of both 12 and that number. For example, the LCM of 12 and 15 is 60.

## How do I know if a number is a multiple of 12?

A number is a multiple of 12 if it is divisible by both 3 and 4. For instance, 96 is a multiple of 12 because it can be divided by 3 (96 ÷ 3 = 32) and by 4 (96 ÷ 4 = 24).

## Can multiples of 12 be negative?

Yes, multiples of 12 can be negative. For example, -12, -24, and -36 are all multiples of 12.

## What is the 10th multiple of 12?

The 10th multiple of 12 is found by multiplying 12 by 10: 12 × 10 = 120

## How are multiples of 12 used in real life?

Multiples of 12 are used in various real-life scenarios, such as scheduling events every 12 days, packaging products in groups of 12, and managing inventory in dozens.

## Are there patterns in the multiples of 12?

Yes, there are patterns in the multiples of 12. Each multiple is 12 units apart from the next, and they follow the sequence 12, 24, 36, 48, 60, etc.

## What are the common multiples of 12 and 8?

Common multiples of 12 and 8 include numbers that are multiples of both 12 and 8. Examples are 24, 48, 72, 96, and 120.