This article is focused on extracting multiples of 3 and finding common multiples of 3 with other numbers such as 4, 5, 7, 8 and 9. Let’s start.

## Multiples of 3

There are millions of multiples can be found through any number. Finding multiples is super easy job, because you have to just keeping multiplying numbers. There are two methods to find multiples of 3. Let’s go through both of the methods to give you clear understanding of multiples.

### Finding Multiples of 3 – Method 1

In this method, you have to start multiplying 3 with 1 and then with 2 and so on. Difficult to understand? Have a look at table below.

Number | Multiplied by | Multiple Extracted |

3 | 1 | 3 |

3 | 2 | 6 |

3 | 3 | 9 |

3 | 4 | 12 |

3 | 5 | 15 |

3 | 6 | 18 |

3 | 7 | 21 |

3 | 8 | 24 |

3 | 9 | 27 |

3 | 10 | 30 |

We found first 10 Multiples of 3 Here are those ones:

### Finding Multiples of 3 – Method 2

It is also easy method. You just have to add 3 with previous number. Ahhh man.! It is difficult. No problem. Let’s have a look at following method

First multiple of 3 will be 3 it self. Now add 3 in it. 3+3 = 6. You got another multiple i.e. 6. Now add 3 in it. 6+3 = 9. You got another multiple i.e. 9. Keep adding 3 and keep extracting thousands of multiples of 3. By the way, we have made a table for you for first few multiples of 3 have a look at those.

### First 100 Multiples of 3

3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |

33 | 36 | 39 | 42 | 45 | 48 | 51 | 54 | 57 | 60 |

63 | 66 | 69 | 72 | 75 | 78 | 81 | 84 | 87 | 90 |

93 | 96 | 99 | 102 | 105 | 108 | 111 | 114 | 117 | 120 |

123 | 126 | 129 | 132 | 135 | 138 | 141 | 144 | 147 | 150 |

153 | 156 | 159 | 162 | 165 | 168 | 171 | 174 | 177 | 180 |

183 | 186 | 189 | 192 | 195 | 198 | 201 | 204 | 207 | 210 |

213 | 216 | 219 | 222 | 225 | 228 | 231 | 234 | 237 | 240 |

243 | 246 | 249 | 252 | 255 | 258 | 261 | 264 | 267 | 270 |

273 | 276 | 279 | 282 | 285 | 288 | 291 | 294 | 297 | 300 |

So, you have list of first 100 multiples of 3 can be used anywhere. If you need more than those just keep adding 3 you will get millions of multiples.

## Common Multiples of 3 and 4 (upto or less than 100)

Now, as we know that how to find multiples of any number we will just move to finding common multiples.

Now, we will have a look at common numbers which are part of both lists. We found following:

So we found 8 common multiples of 3 and 4 upto 100. Here are other notable facts:

- As 3 x 4 = 12, so common multiples of 3 and 4 are all multiples of 12.
- 12 is least common multiple (LCM) of 3 and 4
- All multiples of 3 and 4 are even numbers

## Common Multiples of 3 and 5 upto 100

Now, you know very well about common multiples. These are common numbers which are multiples of both provided numbers. Let’s solve problem now:

Now we will find common Multiples of both numbers we found following ones:

Here are notable facts for these both numbers:

- There are 6 common factors of both numbers
- 15 is least common multiple (LCM) of 3 and 5
- All common multiples are also multiples of 15

## Common Multiples of 3 and 8

Common Multiples of 3 and 8 will be found as follows:

Let’s check for common Numbers now:

Here are few notable points:

- There are four common multiples of 3 and 4 upto 100
- 24 is least common multiple of 3 and 8
- all common multiples of 3 and 8 are even numbers

## Common Multiples of 3 and 7

As 3 and 7 both are odd prime numbers, so, all common multiples will be even as well as odd numbers. Oh dude, everyone knows this. No problem we will be solving this problem with a new technique.

Whenever you have to find common multiples of two numbers you have to follow these steps:

### Multiply 3 and 7 with each other

Let’s multiply given numbers with each other: 3 x 7 = 21

### Find Multiples of that number

Let’s now get Multiples of 21, here are those:

### You got answer

Yes, you heard right, you got the answer. All Multiples of 21 are all common multiples of 3 and 7.

You can follow above steps for common multiples of any 2 numbers### Still confused? Let’s try it in other way:

3 Multiples of 3 = 3, 6, 9, 12, 15, 18,**21**, 24, 27, 30, 33, 36, 39,

**42**, 45, 48, 51, 54, 57, 60,

**63**, 66, 69, 72, 75, 78, 81,

**84**, 87, 90, 93, 96, 99 7 Multiples of 7 = 7, 14,

**21**, 28, 35,

**42**, 49, 56,

**63**, 70, 77,

**84**, 91, 98

Letters in Blue fonts are common in both lists so let’s organise those:

You got same answer.

## Common Multiples of 3 and 6

This set of multiples will be interesting because, I will be providing you another trick for these type of multiples. Read below Knowledge Box before we start with common multiples.

So Let’s start now. Greater number in our case is 6 and it is multiple of 3 also. So we will have to just find multiples of 6 and all of those are common multiples of both numbers. Let’s solve by traditional way:

So you will see all multiples of 6 are also multiples of 3 so multiples of 6 are common multiples of 3 and 6.

Here are few notable points:

- Multiples of 6 are common Multiples of 3 and 6
- 6 is least common multiple (LCM) of both 3 and 6
- All even multiples of 3 are common multiples of 3 and 6.

## Common Multiples of 3 and 9

Let’s solve common Multiples of 3 and 9. As you know 9 is 3rd multiple of 3. So it’s multiples will be common multiples of both numbers. We have tested this in previous question. Here, we will be writing only solution with 100% confidence. You can check it manually also.

Here are few notable points:

- All Multiples of 9 are common multiples of 3 and 9
- LCM (Least common multiple) of 3 and 9 is 9.

## Common Multiples of 3 and 2

Let’s find common multiples of first two prime numbers. As none of these numbers is multiple of others, so, common multiples can be found by multiplying 3 and 2 with each other.

We know that, 3 x 2 = 6

and,

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, …….

so these are common Multiples of 2 and 3:

## Multiples of 3 Song

Here is beautiful song for Multiples of 3 sung by Numberock.

## Conclusion

I am pretty much sure that after reading this post, you will be able to understand the mathematics of multiples and you will be able to find multiples of any number. We just need your help by sharing this post with others and liking and appreciating us if we are able to solve your problem. Have a good day ahead.!

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