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Properties of Multiples

1. Every number other than zero is a multiple of itself.

Examples: Multiples of 4 are 4, 8, 12, 16, ...
Multiples of 5 are 5, 10, 15, 20, ...

Clearly, 4 and 5 are multiples of themselves.

2. Every multiple of a number other than zero is greater than or equal to itself.
Examples: Multiples of 6 are 6, 12, 18, 24, ...

Multiples of 7 are 7, 14, 21, 28, ...
Think Tank Logical Thinking
3. There are an infinite (endless or uncountable) List the first five

number of multiples of a number. multiples of your age and
Examples: Multiples of 7 are 7, 14, 21, 28, ... your friend’s age taking complete
years.
Multiples of 9 are 9, 18, 27, 36, ...
Multiples of 10 are 10, 20, 30, 40, ...

From the above examples, we can say that there are infinite multiples of any given
number.

common Multiples 1 2 3 4 5 6 7 8 9 10

Here the numbers 1 to 60 are shown in 11 12 13 14 15 16 17 18 19 20
the grid. We circle those numbers red 21 22 23 24 25 26 27 28 29 30
which are the multiples of 4 and blue 31 32 33 34 35 36 37 38 39 40
which are the multiples of 6.

Numbers in red circles are: 4, 8, 12, 16, 20, 41 42 43 44 45 46 47 48 49 50

24, 28, 32, 36, 40, 44, 48, 52, 56 and 60. 51 52 53 54 55 56 57 58 59 60
Numbers in blue circles are: 6, 12, 18, 24, 30, 36, 42, 48, 54 and 60.

Numbers in both coloured circles are: 12, 24, 36, 48 and 60.

Thus, the common multiples of 4 and 6 are 12, 24, 36, 48 and 60.

Hence, the numbers which are common among
the multiples of two or more numbers are called Think Tank Logical Thinking
the common multiples. There are 7 days in

Example: Find the common multiples of 2 and 5. a week. Which of the
following numbers of days will
Solution: The multiples of 2 are 2, 4, 6, 8, 10 , form an exact number of weeks?

12, 14, 16, 18, 20 , ... 7, 10, 13, 14, 20, 23, 28, 31
The multiples of 5 are 5, 10 , 15, 20 , 25, 30, 35, ...

The common multiples of 2 and 5 are 10, 20, ...

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