Practice Set 12 Class 7 Answers Chapter 3 HCF and LCM Maharashtra Board 2026-27

Practice Set 12 Class 7 Answers Chapter 3 HCF and LCM Maharashtra Board are prepared by Infinity Learn to help Class 7 students understand HCF and LCM in a simple, step-by-step, and exam-focused way. This content is written for students who want clear solutions for homework, classwork, revision, and exam preparation for the 2026-27 academic session. The answers are based on the Maharashtra Board Class 7 Maths syllabus and the important concepts covered in Chapter 3, so students can learn the correct method and solve similar questions with confidence.

Maharashtra Board Class 7 Maths Chapter 3 HCF and LCM Overview

Chapter 3 of Class 7 Maths introduces students to two important concepts: Highest Common Factor (HCF) and Lowest Common Multiple (LCM). These concepts help students solve problems related to factors, multiples, equal grouping, common timings, and repeated events.

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Practice Set 12 Class 7 Answers with Step-by-Step Solutions

The Practice Set 12 Class 7 Answers Chapter 3 HCF and LCM Maharashtra Board solutions should be written in a clear and simple format so that students can understand the method easily.

Std 7 Maths Practice Set 12 Solutions Answers

Question 1.

i. 25, 40

ii. 56, 32

iii. 40, 60, 75

iv. 16, 27

v. 18, 32,48

vi. 105, 154

vii. 42, 45, 48

viii. 57, 75, 102

ix. 56, 57

x. 777, 315, 588

Solution: 

i. 25, 40

25 = 5 × 5

40 = 2 × 2 × 2 × 5

HCF of 25 and 40 = 5

ii. 56, 32

56 = 2 × 2 × 2 × 7

32 = 2 × 2 × 2 × 2 × 2

HCF of 56 and 32 = 2 × 2 × 2

HCF of 56 and 32 = 8

iii. 40, 60, 75

40 = 2 × 2 × 2 × 5

60 = 2 × 2 × 3 × 5

75 = 3 × 5 × 5

HCF of 40, 60 and 75 = 5

iv. 16, 27

16 = 2 × 2 × 2 × 2 × 1

27 = 3 × 3 × 3 × 1

HCF of 16 and 27 = 1

v. 18, 32,48

18 = 2 × 3 × 3

32 = 2 × 2 × 2 × 2 × 2

48 = 2 × 2 × 2 × 2 × 3

HCF of 18, 32 and 48 = 2

vi. 105, 154

105 = 3 × 5 × 7

154 = 2 × 2 × 11

HCF of 105 and 154 = 7

vii. 42, 45, 48

42 = 2 × 3 × 7

45 = 3 × 3 × 5

48 = 2 × 2 × 2 × 2 × 3

HCF of 42,45 and 48 =3

viii. 57, 75, 102

57 = 3 × 19

75 = 3 × 5 × 5

102 = 2 × 3 × 17

HCF of 57, 75 and 102 = 3

ix. 56, 57

56 = 2 × 2 × 2 × 7 × 1

57 = 3 × 19 × 1

HCF of 56 and 57 = 1

x. 777, 315, 588

777 = 3 × 7 × 37

315 = 3 × 3 × 5 × 7

588 = 2 × 2 × 3 × 7 × 7

HCF of 777, 315 and 588 = 3 × 7

HCF of 777, 315 and 588 = 21

Question 2. Find the HCF by the division method and reduce to the simplest form:

i. 275/525

Solution:

ii. 76/133

Solution:

iii. 161/69

Solution:

Practice Set 12 Class 7 Maths Chapter 3 HCF and LCM Intext Questions and Activities Maharashtra Board

Question 1. In each of the following examples, write all the factors of the numbers and find the greatest common divisor. (Textbook pg. no. 17)

i. 28, 42

Solution: Factors of 28 = 1,2,4, 7, 14, 28

Factors of 42 = 1,2, 3, 6, 7, 14, 21, 42

HCF of 28 and 42 = 14

ii. 51, 27

Solution: Factors of 51 = 1, 3, 17, 51

Factors of 27 = 1, 3, 9, 27

HCF of 51 and 27 = 3

iii. 25, 15, 35

Solution: Factors of 25 = 1, 5, 25

Factors of 15 = 1, 3, 5, 15

Factors of 35 = 1, 5, 7, 35

HCF of 25, 15 and 35 = 5

Important HCF and LCM Formulas for Class 7 Maharashtra Board

Students should remember these important rules while solving Practice Set 12 class 7:

• HCF = Product of common prime factors
• LCM = Product of the highest powers of all prime factors
• For two numbers: HCF × LCM = Product of the two numbers
• HCF is always less than or equal to the smallest given number.
• LCM is always greater than or equal to the largest given number.
• HCF of co-prime numbers is 1.
• LCM of co-prime numbers is the product of the numbers.