# What are the multiples of 3?

## Skip counting by 3’s

Skip counting is the method of skipping certain numbers in the number sequence. To skip count by 3’s start with the number 3 and mark every 3rd number from the given number.

Let us skip count by 3 for the numbers up to 100.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |

51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |

61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |

71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |

81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

The skip counting here also gives the multiples of 3 up to 100.

## Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 …

The multiples of **3** are all the values that we get by multiplying any number by **3**.

The multiples of **3** are the same as the values we get by skip counting by **3**.

**Example:**

The first five multiples of three are obtained by multiplying the numbers up to **5** by **3**.

$$1 \times 3 = 3$$

$$2 \times 3 = 6$$

$$3 \times 3 = 9$$

$$4 \times 3 = 12$$

$$5 \times 3 = 15$$

We can find any number of multiples in a similar manner.

## The nth multiple of 3

We know that we can find any number of multiples of **3** by multiplying the given number by **3**. The value of the multiple of any nth value is given by **3n.**

**Example:**

**Find the 16th multiple of 3.**

The nth multiple of **3** is given by **3n**

The 16th multiple of **3** is given by $$3 \times 16 = 48$$

## Did you know?

**Difference between factors and multiples of 3**

3 is a prime number. The prime numbers are the numbers that are only divisible by 1 and the number itself. Hence the factors of 3 are 1 and 3. The factors are the numbers that a given value can be split into, whereas, the multiples are the values that are obtained by the product of 3 and any other number.

Note that factors of a number are smaller than or equal to the number itself. The multiples of a number are either equal to or bigger than a given number.

Every number is both a factor and a multiple of itself.

### Test of divisibility for 3

The test of divisibility of 3 is the test that we can use to find if a given number is a multiple of 3 or not. In other words, the test of divisibility of 3 helps to determine whether a given number is divisible by 3.

To find if a given number is divisible by 3, find the sum of the digits of the number. If the sum is divisible by 3, then the given number is also divisible by 3.

**Example:**

**Conduct the test of divisibility to find if the given value is divisible by 3.**

**7542**

Here the digits of the number are **7, 5, 4,** and **2**.

The sum of the digits are **7 + 5 + 4 + 2 = 18**

The sum 18 is divisible by **3**, hence the number **7542** is also divisible by **3**.

The test of divisibility is helpful in identifying the multiples of 3 for large numbers

without actually dividing the number by 3.

### Least common multiple:

The least common multiple is the first common multiple of two numbers. To find the least common multiple of two numbers write down the multiples of both the numbers until you find one common multiple.

Let us take the example of two numbers 9 and 12 to find the least common mulitple.

Multiples of 9: 9, 18, 27, **36**, 45, 54, 63, 72, 81,90

Multiples of 12: 12, 24, **36**, 48, 60, 72

We can see that 36 is the first common multiple that appears in the multiples sequence.

#### Hence 36 is the first common multiple of 9 and 12.

Note that there will be other multiples that are common to the multiples sequence of both the numbers. But the multiple that is common and occurs first is called the least common multiple.

The least common multiples are helpful in finding the common denominator in fraction addition and subtraction.