Did you know that the sum of all the digits of the multiples of 9 add up to 9. For example, 18 is a multiple of 9 and 1 + 8 = 9. Similarly, 198 is a multiple of 9 and 1 + 9 + 8 = 18 and 1 + 8 = 9. Isn”t this interesting?** **In this mini-lesson, we will calculate the multiples of 9 and we will learn some interesting facts about these multiples with solved examples and interactive questions.

You are watching: What is a multiple of 9

**First five multiples of 9**: 9, 18, 27, 36, 45**Prime Factorization of 9**: 9 = 3 × 3 = 32

1. | What Are the Multiples of 9? |

2. | First 20 Multiples of 9 |

3. | Tips and Tricks |

4. | FAQs on Multiples of 9 |

5. | Thinking Out of The Box! |

## What Are the Multiples of 9?

The multiples of 9 are the numbers which are obtained by multiplying 9 with integers. When we multiply 9 with a positive integer, we get a positive multiple of 9 and when we multiply 9 with a negative integer, we will obtain negative multiples. We don”t include fractions when finding multiples. For Example: 9 × 4 = 36

Here, 36 is a multiple of 9. We have learnt that 9 and 4 are called factors of 36. We can also say that 36 is one of the multiples of 4. The other multiples of 4 can be obtained by multiplying 4 with integers.

## List of First 20 Multiples of 9

Multiplication is repeated addition. For example, 9 + 9 = 2 × 9 = 18 and 9 + 9 + 9 + 9 = 4 × 9 = 36 Thus, 18 and 36 are the 2nd and 4th multiples of 9 respectively, which can be obtained by adding 9 repeatedly or by simply multiplying 9 with the integers 2 and 4. The other way is to multiply 9 with natural numbers 1, 2, 3, etc. The multiples of 9 are innumerable as there are infinitely many integers. Let”s find the first 20 multiples of 9 by multiplying 9 by each of the natural numbers from 1 to 20.

See more: What Does Gm Stand For In Weight ? Medical Definition Of Gm (Gram)

Multiply 9 by the numbers from 1 to 20

Multiples of 9

9 × 1 | 9 |

9 × 2 | 18 |

9 × 3 | 27 |

9 × 4 | 36 |

9 × 5 | 45 |

9 × 6 | 54 |

9 × 7 | 63 |

9 × 8 | 72 |

9 × 9 | 81 |

9 × 10 | 90 |

9 × 11 | 99 |

9 × 12 | 108 |

9 × 13 | 117 |

9 × 14 | 126 |

9 × 15 | 135 |

9 × 16 | 144 |

9 × 17 | 153 |

9 × 18 | 162 |

9 × 19 | 171 |

9 × 20 | 180 |

**To understand the concept of finding multiples, let us look at a few more examples.**

**Tips and Tricks:**

Two numbers that are made up of the same set of digits will have a difference, which is a multiple of 9.This property holds true for all numbers made up of the same digits. For example: Consider the numbers 45268 and 86254. Both are made up of the same digits.86254 – 45268 = 40986 and 40986 = 4554 × 9 which shows that the difference, i.e. 40986, is a multiple of 9.

**Think Tank:**

For the pair (9, 36), the LCM is 36. Similarly, the LCM of (12, 36) is 36. Based on this information, can you identify the property which a number and its multiple has?What will be the GCF of the above numbers and how is it related to their LCM?

**Example 1:** Ms. Cathy wants to arrange 108 children in groups of 9. Is it possible for her to do such an arrangement without leaving out any child? How many groups will be formed here?

**Solution**:

To check whether any child will be left or not, we need to verify if 108 is divisible by 9 or not.Sum of digits in 108 = 1 + 0 + 8 = 9, which is a multiple of 9.Recall: If the sum of all the digits of a number is divisible by 9, then the given number is also divisible by 9. Thus, 108 is divisible by 9.

That means, no child will be left if the students are arranged in a group of 9. From the information 9 × 12 = 108.

Hence, there will be 12 groups with 9 students in each group.

**Example 2:** Mia and Joe have the same number of cards. Mia arranges her cards in rows of 9 each, whereas Joe arranges his cards in rows of 8 each. What is the minimum number of cards they can have?

**Solution**:

To get the minimum number of cards, we need to find the least common multiple of 9 and 8. Let”s list the first 10 multiples of 9 and 8.

See more: What Is The Coefficient Of O2 When The Equation Is Completely Balanced

Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

We observe that 72 is the number that is a common multiple of 9 and 8. As we continue listing the multiples, we will get many more common multiples. Out of those, 72 is the least common multiple.

## Discussion about this post