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Multiple Properties

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, numbers 4 and 5 are the multiples of itself.

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 and Answer
3. There are infinite (endless or uncountable) number List the first five

of multiples of a number. multiples of your age and
examples: Multiples of 7 are 7, 14, 21, 28, ... your friend’s age taking in
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 1 2 3 4 5 6 7 8 9 10

given number. 11 12 13 14 15 16 17 18 19 20
common Multiples 21 22 23 24 25 26 27 28 29 30

Here, numbers 1 to 60 are shown in the 31 32 33 34 35 36 37 38 39 40
grid. We circle the numbers red which 41 42 43 44 45 46 47 48 49 50
are the multiples of 4 and blue which are 51 52 53 54 55 56 57 58 59 60

the multiples of 6.

Numbers in red circles are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56 and 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 and Answer
the common multiples. There are 7 days in a week.
Which of the following
example: Find the common multiples of 2 and 5. number of days will form

Solution: The multiples of 2 are 2, 4, 6, 8, 10 , 12, exact number of weeks?
7, 10, 13, 14, 20, 23, 28, 31.
14, 16, 18, 20 , ...

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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