Maharashtra Board Solutions Class 7-Maths (Practice Set 13): Chapter 3- HCF and LCM

Class 7: Maths Chapter 3 solutions. Complete Class 7 Maths Chapter 3 Notes.

Maharashtra Board Solutions Class 7-Maths (Practice Set 13): Chapter 3- HCF and LCM

Maharashtra Board 7th Maths Chapter 3, Class 7 Maths Chapter 3 solutions

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

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Maharashtra Board Solutions Class 7-Maths (Practice Set 13): Chapter 3- HCF and LCM

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Chapterwise Maharashtra Board Solutions Class 7 Maths :

• Chapter 1- Geometrical Constructions (Practice Set 1)
• Chapter 1- Geometrical Constructions (Practice Set 2)
• Chapter 1- Geometrical Constructions (Practice Set 3)
• Chapter 1- Geometrical Constructions (Practice Set 4)
• Chapter 1- Geometrical Constructions (Practice Set 5)
• Chapter 1- Geometrical Constructions (Practice Set 6)
• Chapter 1- Geometrical Constructions (Practice Set 7)
• Chapter 2- Multiplication and Division of Integers (Practice Set 8)
• Chapter 2- Multiplication and Division of Integers (Practice Set 9)
• Chapter 3- HCF and LCM (Practice Set 10)
• Chapter 3- HCF and LCM (Practice Set 11)
• Chapter 3- HCF and LCM (Practice Set 12)
• Chapter 3- HCF and LCM (Practice Set 13)
• Chapter 3- HCF and LCM (Practice Set 14)
• Chapter 4- Angles and Pairs of Angles (Practice Set 15)
• Chapter 4- Angles and Pairs of Angles (Practice Set 16)
• Chapter 4- Angles and Pairs of Angles (Practice Set 17)
• Chapter 4- Angles and Pairs of Angles (Practice Set 18)
• Chapter 4- Angles and Pairs of Angles (Practice Set 19)
• Chapter 4- Angles and Pairs of Angles (Practice Set 20)
• Chapter 4- Angles and Pairs of Angles (Practice Set 21)
• Chapter 5- Operations on Rational Numbers (Practice Set 22)
• Chapter 5- Operations on Rational Numbers (Practice Set 23)
• Chapter 5- Operations on Rational Numbers (Practice Set 24)
• Chapter 5- Operations on Rational Numbers (Practice Set 25)
• Chapter 6- Indices (Practice Set 26)
• Chapter 6- Indices (Practice Set 27)
• Chapter 6- Indices (Practice Set 28)
• Chapter 6- Indices (Practice Set 29)
• Chapter 6- Indices (Practice Set 30)
• Chapter 7- Joint Bar Graph (Practice Set 31)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 32)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 33)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 34)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 35)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 36)
• Chapter 9- Direct Proportion and Inverse Proportion (Practice Set 37)
• Chapter 9- Direct Proportion and Inverse Proportion (Practice Set 38)
• Chapter 9- Direct Proportion and Inverse Proportion (Practice Set 39)
• Chapter 10- Bank and Simple Interest (Practice Set 40)
• Chapter 10- Bank and Simple Interest (Practice Set 41)
• Chapter 11- Circle (Practice Set 42)
• Chapter 11- Circle (Practice Set 43)
• Chapter 12- Perimeter and Area (Practice Set 44)
• Chapter 12- Perimeter and Area (Practice Set 45)
• Chapter 12- Perimeter and Area (Practice Set 46)
• Chapter 12- Perimeter and Area (Practice Set 47)
• Chapter 13- Pythagoras Theorem (Practice Set 48)
• Chapter 13- Pythagoras Theorem (Practice Set 49)
• Chapter 14- Algebraic Formulae - Expansion of Squares (Practice Set 50)
• Chapter 14- Algebraic Formulae - Expansion of Squares (Practice Set 51)
• Chapter 14- Algebraic Formulae - Expansion of Squares (Practice Set 52)
• Chapter 14- Algebraic Formulae - Expansion of Squares (Practice Set 53)
• Chapter 15- Statistics (Practice Set 54)
• Chapter 14- Statistics (Practice Set 55)