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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 :
