# Mathsight Class 6 Solutions Chapter 3

## 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 :

Updated: May 25, 2023 — 4:18 pm