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**Mathsight Class 6 Solutions Chapter 3 HCF and LCM**

Welcome to NCTB Solutions. Here with this post we are going to help 6th class students to solve MathSight Class 6 Mathematics Book, Chapter 3, HCF and LCM. Here students can easily get all the exercise questions solution for Chapter 3, HCF and LCM Exercise 3.1, 3.2, 3.3 and 3.4

**HCF and LCM Exercise 3.1 Solution : **

**Question no – (1)**

**Solution :**

(3,5), (5,7), (17,19), (11,13)

**Question no – (2)**

**Solution :**

(2,3), (3,4), (5,6), (7,8)

**Question no – (3)**

**Solution : **

**(b)** 12 = 3 × 4

60 = 3 × 4 × 5

**(c)** 13 = 13 × 1

78 = 13 × 6

**(d)** 24 = 6 × 4

36 = 6 × 6

**Question on – (4)**

**Solution : **

**(a)** 23

= 2 + 5 +13

**(b)** 41

= 11 + 13 + 17

**(c)** 59

= 29 + 13 + 17

**(d)** 91

= 71 + 3 + 17

**Question no – (5)**

**Solution :**

There are 25 prime numbers between 1 to 100.

**Question no – (6)**

**Solution :**

There are only 1 even prime number in the set of natural numbers.

**Question no – (7)**

**Solution :**

3 + 7 = 10

9 + 3 = 12

17 + 13 = 30

31 + 39 = 70

83 + 89 = 172

**Question no – (8)**

**Solution :**

Yes, 34212 is a multiple of 12

**Question no – (9)**

**Solution :**

12 as the product of prime numbers,

∴ 120 = 2 × 2 × 2 × 3 × 5

**Question no – (10)**

**Solution :**

2 + 2 = 4

2 × 2 = 4

∴ Number is ‘22’

**Question no – (11)**

**Solution : **

11 m 50 cm = 1650 cm.

15 m 25 cm. = 1525 cm.

∴ 1650 = 2 × 5 × 5 × 33

1525 = 5 × 5 × 61

∴ HCF = 5

∴ 5 = 25

∴ Required number will be,

= 1650 × 1525/25

= 99330

**Question no – (12)**

**Solution :**

(a) 60 = 58 + 2

(b) 60 = 47 + 13

(c) 60 = 30 × 2

(d) 60 = 12 × 5

**HCF and LCM Exercise 3.2 Solution : **

**Question no – (1)**

**Solution :**

(a) 281410

(b) No

(c) 12263

(d) No

**Question no – (2)**

**Solution :**

(a) No

(b) 17707

(c) No

(d) 5748

**Question no – (3)**

**Solution :**

(a) 5,820

(b) 90,202

(c) No

(d) No

**Question no – (4)**

**Solution :**

(a) 6,189

(b) 31,092

(c) No

(d) 12,082

**Question no – (5)**

**Solution :**

(a) 79,111

(b) 15,504

(c) No

(d) 61516

**Question no – (6)**

**Solution :**

(a) by 5 ⇒ 5407

By 10 ⇒ No

(b) by 5 ⇒ 13718

By 10 ⇒ 6859

(c) by 5 ⇒ 297519

By 10 ⇒ No

(d) by 5 ⇒ No

By 10 ⇒ No

**Question no – (7)**

**Solution :**

(a) 1546

(b) No

(c) No

(d) 1836

**Question no – (8)**

**Solution :**

(a) 3456

(b) 20916

(c) 22448

(d) No

**Question no – (9)**

**Solution :**

(a) 4

(b) 3

(c) 9

(d) 8

**Question no – (10)**

**Solution :**

By 8 => 216

By 9 => 192

**Question no – (11)**

**Solution :**

13 + 3 = 16

5 + 3 = 8

5 + 11 = 16

5 + 7 = 12

3 + 17 = 20

**Question no – (12)**

**Solution :**

888 + 88 + 8 + 8 + 8 = 1000

**Question no – (13)**

**Solution :**

121 ÷ 11 = 11

Similarly = 121 ÷ 11 = 11

∵ Digit of odd place = 1 + 1 = 2

Digit of eve place = 2

Difference of than,

= 2 – 2

= 0

**HCF and LCM Exercise 3.3 Solution : **

**Question no – (1)**

**Solution : **

(a) 216

= 2 × 2 × 2 × 3 × 3 × 3

(b) 132

= 2 × 2 × 3 × 11

(c) 512

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

(d) 630

= 2 × 3 × 3 × 5 × 7

(e) 372

= 2 × 3 × 31

**Question no – (2)**

**Solution : **

(a) 44

= 2 × 2 × 11

72 = 2 × 2 × 2 × 3 × 3

∴ CF = 2 × 2

= 4

(b) 48 = 2 × 2 × 2 × 2× 3

64 = 2 × 2 × 2 × 2 × 2 × 2

∴ CF = 2 × 2 × 2 × 2

= 16

(c) 75 = 5 × 5 × 3

105 = 3 × 5 × 7

∴ CF = 3 × 5

= 15

(d) 18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

∴ CF = 2 × 3

= 6

(e) 32 = 2× 2 × 2× 2 × 2

48 = 2 × 2 × 2 × 2 × 2 × 3

∴ CF = 2 × 2 × 2 × 2 × 2

= 32

**Question no – (3)**

**Solution : **

(a) 28 = 2 × 2 × 7

118 = 2 × 59

∴ HCF = 2

(b) 27 = 3 × 7

102 = 3 × 2 × 17

∴ HCF = 3

(c) 250 = 2 × 5 × 5 × 5

450 = 2 × 5 × 5 × 3 × 3

∴ HCF = 2 × 5 × 5 = 50

(d) 144 = 3 × 3 × 2 × 2 × 2 × 2

372 = 3 × 2 × 2 × 31

∴ HCF = 3 × 2 × 2 = 12

(e) 25 = 2 × 5

27 = 3 × 3 × 3

H.C.F = 1

**Question no – (4)**

**Solution : **

(a) 575, 920

∴ HCF = 5

(b) 240, 1024

∴ HDF = 16

(c) 1379, 2401

∴ HDF = 7

(d) 320, 420, 180

∴ HDF = 20

**Question no – (5)**

**Solution :**

36, 81, 108

∴ HDF = 9

**Question no – (6)**

**Solution : **

∵ leaving a remainder 5 in each case –

∴ 89 – 5 = 84

53 – 5 = 48

77 – 5 = 72

84 = 2 × 2 × 3 × 7

48 = 2 × 2 × 2 × 2 × 3

72 = 2 × 2 × 2 × 3 × 3

∴ HDF = 3 × 2 × 2

= 12

**Question no – (7)**

**Solution :**

78 – 3 = 75

230 – 5 = 225

682 – 7 = 675

∴ HDF = 75

**Question no – (8)**

**Solution : **

247 – 7

= 240

1031 – 7

= 1024

240 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

∴ HDF = 2 × 2 × 2 × 2

= 16

**Question no – (9)**

**Solution : **

360 = 2 × 2 × 2 × 3 × 3 ×5

405 = 3 × 3 × 3 × 3 × 5

495 = 3 × 3 × 11 × 5

∴ HDF = 3 × 3 × 5

= 45

**Question no – (10)**

**Solution :**

76 – 4 = 72

113 – 5 = 108

186 – 6 = 180

72 = 2 × 2 × 2 × 3 × 3

108 = 2 × 2 × 3 × 3 × 3

180 = 2 × 2 × 5 × 3 × 3

∴ HDF = 2 × 2 × 3 × 3

= 36

**Question no – (11)**

**Solution :**

Max number of Friday = 50/7

= 7.14 ≈ 7

**Question no – (12)**

**Solution :**

(i) 48, 264, 240

(ii) 72, 120, 168

(iii) 96, 192, 144

**HCF and LCM Exercise 3.4 Solution : **

**Question no – (1)**

**Solution :**

**(a)** 12 = 2 × 2 × 3

42 = 2 × 3 × 7

LCM = 2 × 3 × 2 × 7

= 84

**(b)** 45 = 5 × 3 × 3

70 = 5 × 2 × 7

90 = 5 × 2 × 3 × 3

LCM = 5 × 2 × 3 × 3 × 7

= 630

**(c)** 36 = 2 × 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

60 = 2 × 3 × 2 × 5

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5

= 720

**(d)** 22 = 2 × 11

44 = 2 × 2 × 11

66 = 2 × 3 × 11

LCM = 2 × 11 × 2 × 3

= 132

**Question no – (2)**

**Solution :**

**(a)** 24, 27, 30, 90

∴ LCM = 3 × 2 × 3 × 5 × 4 × 3

= 1080

**(b)** 30, 48, 120

∴ LCM = 6 × 4 × 5 × 2

= 240

**(c)** 72, 96, 108

∴ LCM = 12 × 3 × 2 × 4 × 3

= 864

**(d)** 40, 80, 100, 120

∴ LCM = 10 × 2 × 2 × 2 × 5 × 3

= 1200

**Question no – (3)**

**Solution :**

**(a)** 3 = 3 × 1

4 = 2 × 2

LCM = 3 × 2 × 2

= 12

**(b)** 4 = 2 × 2

12 = 2 × 2 × 3

LCM = 2 × 2 × 3

= 12

**(c)** 8 = 2 × 2 × 2

12 = 2 × 2 × 3

LCM = 2 × 2 × 2 × 3

= 24

**(d)** 15 = 3 × 5

20 = 2 × 2 × 5

= 60

**Question no – (4)**

**Solution : **

**(a)** 13 = 13 × 1

52 = 13 × 4

∴ HCF = 13

LCM = 13 × 4

= 52

∴ Product = 13 × 52

= 676

= 13 × 52

**(b)** 21 = 3 × 7

27 = 3 × 3 × 3

HCF = 3

LCM = 3 × 3 ×3 × 7

= 189

∴ Product = 567

= 21 × 27

**(c)** 120 = 3 × 2 × 2 × 2 × 5

35 = 5 × 7

∴ 120 = 3 × 2 × 2 × 2 × 5

35 = 5 × 7

∴ HCF = 5

LCM = 5 × 3 × 2 × 2 × 2 × 7

= 840

∴ Product = 4200

= 120 × 35

**(d)** 135 = 5 × 3 × 3 × 3

162 = 2 × 3 × 3 × 3 × 3

∴ HCF = 3 × 3 × 3

= 27

LCM = 3 × 3 × 3 × 3 × 2 × 5

= 810

∴ Product = 810 × 27

= 21870

= 130 × 162

**Question no – (5)**

**Solution :**

HCF = 800/400

= 2

**Question no – (6)**

**Solution : **

LCM = 2880/12

= 240

**Question no – (7)**

**Solution :**

Given, 35, 56, 105

∴ LCM = 7 × 5 × 8 × 3

= 840

∴ Required number

= 840 + 5

= 845

**Question no – (8)**

**Solution : **

Given, 36, 40, 45

∴ LCM = 9 × 4 × 5 × 2

= 360

∴ Multiple of 360 = 360, 720, 1080

∴ 4 digit number = 1080

**Question no – (9)**

**Solution : **

Given, 15, 18, 24

∴ LCM = 3 × 2 × 5 × 3 × 4

= 360

∴ Multiple of 360 = 36000

∴ 5 digit number = 36000

**Question no – (10) **

**Solution : **

Given, 8, 10, 12, 14

∴ LCM = 2 × 2 × 2 × 5 × 3 × 7

= 840 min .

∴ time = 840/60

= 14 hr

∴ 7 AM + 14hr = 9 p.m.

**Question no – (11)**

**Solution : **

43512

**Question no – (12)**

**Solution :**

Let, one Number = x

Another number = y

∴ x = 15 – 6

= 9

Two number = 6,9

6 = 3 × 2

9 = 3 × 3

∴ HCF = 3

LCF = 3 × 3 × 2

= 18

**Previous Chapter Solution : **