Question 1.

Find the LCM:

i. 12, 15

ii. 6, 8, 10

iii. 18, 32

iv. 10, 15, 20

v. 45, 86

vi. 15, 30, 90

vii. 105, 195

viii. 12,15,45

ix. 63,81

x. 18, 36, 27

Solution:

i. 12, 15

∴ LCM of 12 and 15 = 3 x 2 x 2 x 5

= 60

ii. 6, 8, 10

∴ LCM of 6, 8 and 10 = 2 x 2 x 3 x 2 x 5

= 120

iii. 18, 32

∴ LCM of 18 and 32 = 2 x 2 x 2 x 2 x 3 x 3 x 2

= 288

iv. 10, 15, 20

∴ LCM of 10, 15 and 20 = 5 x 2 x 3 x 2

= 60

v. 45, 86

∴ LCM of 45 and 86 = 2 x 3 x 3 x 5 x 43

= 3870

vi. 15, 30, 90

∴ LCM of 15,30 and 90 = 3 x 5 x 2 x 3

= 90

vii. 105, 195

∴ LCM of 105 and 195 = 5 x 3 x 7 x 13

= 1365

viii. 12, 15, 45

∴ LCM of 12, 15 and 45 = 3 x 3 x 2 x 5 x 2

= 180

ix. 63, 81

∴ LCM of 63 and 81 = 3 x 3 x 3 x 7 x 3

= 567

x. 18, 36, 27

∴ LCM of 18, 36 and 27 = 3 x 3 x 2 x 2 x 3

= 108

Question 2.

Find the HCF and LCM of the numbers given below. Verify that their product is equal to the product of the given numbers:

i. 32, 37

ii. 46, 51

iii. 15, 60

iv. 18, 63

v. 78, 104

Solution:

i. 32 = 2 x 16

= 2 x 2 x 8

= 2 x 2 x 2 x 4

= 2 x 2 x 2 x 2 x 2 x 1

37 = 37 x 1

∴ HCF of 32 and 37 =1

LCM of 32 and 37 = 2 x 2 x 2 x 2 x 2 x 37

= 1184

HCF x LCM = 1 x 1184

= 1184

Product of the given numbers = 32 x 37

= 1184

∴ HCF x LCM = Product of the given numbers.

ii. 46 = 2 x 23 x 1

51 = 3 x 17 x 1

∴ HCF of 46 and 51 = 1

LCM of 46 and 51 = 2 x 23 x 3 x 17

= 2346

HCF x LCM = 1 x 2346

= 2346

Product of the given numbers = 46 x 51

= 2346

∴ HCF x LCM = Product of the given numbers.

iii. 15 = 3 x 5

60 = 2 x 30

= 2 x 2 x 15

= 2 x 2 x 3 x 5

∴ HCF of 15 and 60 = 3 x 5

= 15

LCM of 15 and 60 = 3 x 5 x 2 x 2

= 60

HCF x LCM = 15 x 60

= 900

Product of the given numbers = 15 x 60

= 900

∴ HCF x LCM = Product of the given numbers.

iv. 18 = 2 x 9

= 2 x 3 x 3

63 = 3 x 21

= 3 x 3 x 7

∴ HCF of 18 and 63 = 3 x 3

= 9

LCM of 18 and 63 = 3 x 3 x 2 x 7

= 126

HCF x LCM = 9 x 126

= 1134

Product of the given numbers = 18 x 63

= 1134

∴ HCF x LCM = Product of the given numbers.

v. 78 = 2 x 39

= 2 x 3 x 13

104 = 2 x 52

= 2 x 2 x 26

= 2 x 2 x 2 x 13

∴ HCF of 78 and 104 = 2 x 13

= 26

LCM of 78 and 104 = 2 x 13 x 3 x 2 x 2

= 312

HCF x LCM = 26 x 312

= 8112

Product of the given numbers = 78 x 104

= 8112

∴ HCF x LCM = Product of the given numbers.

**Intext Questions and Activities**

Question 1.

Write the tables of the given numbers and find their LCM. (Textbook pg. no. 19)

i. 6, 7

ii. 8, 12

iii. 5, 6, 15

Solution:

i. Multiples of 6 : 6, 12, 18, 24, 30, 36, 42

Multiples of 7 : 7, 14, 21, 28, 35, 42, 49

∴ LCM of 6 and 7 = 42

ii. Multiples of 8 : 8, 16, 24, 32, 40

Multiples of 12 : 12, 24, 36, 48

∴ LCM of 8 and 12 = 24

iii. Multiples of 5 : 5, 10, 15, 20, 25, 30, 35

Multiples of 6 : 6, 12, 18, 24, 30, 36

Multiples of 15 : 15, 30, 45, 60

∴ LCM of 5,6 and 15 = 30