Page 37 - SM Class 5 Inner.cdr

e. 34, 102 f. 15, 25 and 30 g. 8 and 12 h. 31 and 21
i. 13, 17 and 19 j. 160 and 120

2. What is the HCF of two consecutive (a) numbers ? (b) even numbers ?

3. Which of the following numbers have HCF 1 ?
a. 12 and 15 b. 30 and 60
c. 19 and 21 d. 27 and 54

L.C.M. (Least Common Multiple)

Common multiples of two or more given numbers are the numbers which can
exactly be divided by each of the given numbers, lowest multiple is called the
L.C.M. of those numbers.

Consider the following :
(i) Multiples of 3 are : 3, 6, 9, 12, 15, 18, 21, 24, __________ etc.
Multiples of 4 are : 4, 8, 12, 16, 20, 24, 28, __________ etc.

Therefore, common multiples of 3 and 4 = 12, 24, __________ etc.

It can easily be seen that each of the common multiples 12, 24, etc.,
is exactly divisible by both 3 and 4.

(ii) Multiples of 2 are : 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, __________ etc.
Multiples of 5 are : 5, 10, 15, 20, 25, __________ etc.
Therefore, common multiples of 2 and 5 = 10, 20, __________ etc.

It can easily be seen that each of the common multiples 10, 20, etc.,
is exactly divisible by both 2 and 5.

(iii) Multiples of 2 are : 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, __________ etc.
Multiples of 3 are : 3, 6, 9, 12, 15, 18, 21, 24, __________ etc.

Multiples of 6 are : 6, 12, 18, 24, __________ etc.
Therefore, common multiples of 2, 3 and 6 = 6, 12, 18, 24, __________ etc.

It can easily be seen that each of the common multiples 6, 12, 18, 24, etc.,
is exactly divisible by all three numbers 2, 3 and 6.

The lowest common multiple from these multiples is called their L.C.M.

Methods of finding LCM

1. Prime Factorization Method 2. Division Method

1. LCM using Prime Factorization Method
To find least common multiple by using prime factorization method resolve each
given number into its prime factors and express in factor form.

Then multiply each factor, the greatest number of times it occurs in either
number.
37
Mathematics In Focus - 5