The **Multiples of 6**
are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, … i.e. M_{6} = {6, 12, 18, 24,
30, 36, 42, 48, 54, 60, …}. Multiples of 6 are the series of numbers obtained
by multiplying 6 with the natural numbers.

6 × 1 = 6

6 × 2 = 12

6 × 3 = 18

6 × 4 = 24

6 × 5 = 30

6 × 6 = 36

6 × 7 = 42

6 × 8 = 48

6 × 9 = 54

6 × 10 = 60

…

And so on.

From this series, we observe that the multiples of 6 can be
derived by multiplying 6 by natural numbers in ascending order. These multiples
form an arithmetic sequence with a common difference of 6.

**Properties and
Patterns of Multiples of 6**

Multiples of 6 possess several interesting properties that make
them unique. Here are a few notable ones:

1. __Divisibility by 6__: Every multiple of 6 is divisible by 6 without leaving a
remainder. This property stems from the fact that when we divide any multiple
of 6 by 6, the quotient is always an integer.

2. __Divisibility by 2 and
3__: Since 6 is divisible by both 2 and 3, all multiples of 6 are
also divisible by both 2 and 3. Divisibility by 2 implies that all multiples of
6 are even numbers, while divisibility by 3 suggests that the sum of the digits
of any multiple of 6 is also divisible by 3.

3. __Repeating Pattern of
Digits__: When we examine the units digit of
multiples of 6, a fascinating pattern emerges. The units digit repeats in a
cycle of 6, 2, 8, 4, 0, and again 6, as we proceed to higher multiples. For
instance, the units digit of 6 is 6, the units digit of 12 is 2, and so on.

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**Applications of
Multiples of 6**

The study of multiples of 6 finds applications in various
fields, including mathematics, science, and everyday life:

1. __LCM__: One of the applications of multiples of 6 is in finding the lowest
common multiple (LCM) of two or more numbers. The LCM is the lowest multiple
that two or more numbers have in common. For example, to find the LCM of 6 and 4,
we need to find the multiples of both numbers and identify the lowest multiple
they have in common. The multiples of 6 are 6, 12, 18,
24, 30, 36, 42, 48, 54, 60, … etc. The multiples of 4 are 4, 8, 12, 16, 20, 24,
28, 32, 36, 40 … etc. The lowest multiple that they have in common is 12.
Therefore, the LCM of 6 and 4 is 12.

2. __Timekeeping__: The division of an hour into 60 minutes and each minute into
60 seconds is based on the concept of multiples. By dividing 60 by 6, we obtain
10, which corresponds to the number of minutes in one-tenth of an hour.

3. __Music__: In music theory, multiples of 6 play a crucial role in
understanding rhythm. The time signatures and beats per measure are based on
multiples of 6, allowing musicians to create harmonious compositions.

**Conclusion:**

The **Multiples
of 6** are the numbers obtained by multiplying 6 with natural numbers.
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42,
48, 54, 60, … etc. The multiples of 6 have various properties, such as divisibility
by 6, divisibility by 2 and 3, repeating pattern of digits, etc. The multiples
of 6 have several applications in mathematics, such as finding the LCM,
timekeeping, and music.

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