Page 81 - ICSE Math 4

• Every number is the fi rst and the smallest mul ple of itself.
For example, the fi rst and the smallest mul ple of 9 is 9 and of 12 is 12.

• A number can have infi nite mul ples.

For example, 2, 4, 6, 8, 10, 12, 14, …, and so on are the mul ples of 2.
• Every mul ple of a number is exactly divisible by that par cular number.

For example, 8 ÷ 4 = 2, 15 ÷ 5 = 3 and 27 ÷ 9 = 3.
• The mul ples of a number are either greater than or equal to that number.

For example, 13 × 1 = 13, 13 × 2 = 26, 13 × 3 = 39, and so on. Here, the mul ples of
13 are equal to and greater than 13 but not less than 13.

Common Multiples

When a par cular number is a mul ple of two or more numbers, it is called a common
mul ple.
Remember
To fi nd the common mul ples of the given numbers, follow
the given steps. The smallest multiple
that is common to all
• First list the mul ples of each number. given numbers is called the
• Con nue lis ng the mul ples of each number un l at least common multiple
or L.C.M. of the given
least two mul ples that are common to all the lists of
numbers.
the given numbers are obtained.
Finally, compare and iden fy the common mul ples.

Example 7: Find two common mul ples of 2, 3 and 4.

Solu on: Mul ples of 2 are 2, 4, 6, 8, 10, 12 , 14, 16, 18, 20, 22, 24 , 26, …

Mul ples of 3 are 3, 6, 9, 12 , 15, 18, 21, 24 , 27, …
Mul ples of 4 are 4, 8, 12 , 16, 20, 24 , 28, …

So, the two common mul ples of 2, 3 and 4 are 12 and 24.

Exercise 7.2

1. Fill in the blanks.

(a) Every number is a ____________ of 1.

(b) The mul ples of any number are ____________ or equal to that par cular
number.
(c) The mul ples of 9 ll 81 are _______________________________.

(d) A number can have ____________ mul ples.

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