Get the most accurate MSBSHSE Solutions for Class 7 Maths Chapter 3 Set 13 HCF and LCM here. Updated for the 2026-27 academic session, these solutions are based on the latest MSBSHSE textbooks for Class 7 Maths. Our expert-created answers for Class 7 Maths are available for free download in PDF format.
Detailed Chapter 3 Set 13 HCF and LCM MSBSHSE Solutions for Class 7 Maths
For Class 7 students, solving MSBSHSE textbook questions is the most effective way to build a strong conceptual foundation. Our Class 7 Maths solutions follow a detailed, step-by-step approach to ensure you understand the logic behind every answer. Practicing these Chapter 3 Set 13 HCF and LCM solutions will improve your exam performance.
Class 7 Maths Chapter 3 Set 13 HCF and LCM MSBSHSE Solutions PDF
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
Answer:
(i) 12, 15
| 3 | 12 | 15 |
| 2 | 4 | 5 |
| 2 | 5 |
\( \therefore \) LCM of 12 and 15 = 3 x 2 x 2 x 5
= 60
(ii) 6, 8, 10
| 2 | 6 | 8 | 10 |
| 2 | 3 | 4 | 5 |
| 3 | 2 | 5 |
\( \therefore \) LCM of 6, 8 and 10 = 2 x 2 x 3 x 2 x 5
= 120
(iii) 18, 32
| 2 | 18 | 32 |
| 2 | 9 | 16 |
| 2 | 9 | 8 |
| 2 | 9 | 4 |
| 3 | 9 | 2 |
| 3 | 2 |
\( \therefore \) LCM of 18 and 32 = 2 x 2 x 2 x 2 x 3 x 3 x 2
= 288
(iv) 10, 15, 20
| 5 | 10 | 15 | 20 |
| 2 | 2 | 3 | 4 |
| 1 | 3 | 2 |
\( \therefore \) LCM of 10, 15 and 20 = 5 x 2 x 3 x 2
= 60
(v) 45, 86
| 2 | 45 | 86 |
| 3 | 45 | 43 |
| 3 | 15 | 43 |
| 5 | 43 |
\( \therefore \) LCM of 45 and 86 = 2 x 3 x 3 x 5 x 43
= 3870
(vi) 15, 30, 90
| 3 | 15 | 30 | 90 |
| 5 | 5 | 10 | 30 |
| 2 | 1 | 2 | 6 |
| 1 | 1 | 3 |
\( \therefore \) LCM of 15,30 and 90 = 3 x 5 x 2 x 3
= 90
(vii) 105, 195
| 3 | 105 | 195 |
| 5 | 35 | 65 |
| 7 | 13 |
\( \therefore \) LCM of 105 and 195 = 5 x 3 x 7 x 13
= 1365
(viii) 12, 15, 45
| 3 | 12 | 15 | 45 |
| 3 | 4 | 5 | 15 |
| 5 | 4 | 5 | 5 |
| 2 | 4 | 1 | 1 |
| 2 | 2 | 1 | 1 |
| 1 | 1 | 1 |
\( \therefore \) LCM of 12, 15 and 45 = 3 x 3 x 5 x 2 x 2
= 180
(ix) 63, 81
| 3 | 63 | 81 |
| 3 | 21 | 27 |
| 3 | 7 | 9 |
| 7 | 3 |
\( \therefore \) LCM of 63 and 81 = 3 x 3 x 3 x 7 x 3
= 567
(x) 18, 36, 27
| 3 | 18 | 36 | 27 |
| 3 | 6 | 12 | 9 |
| 2 | 2 | 4 | 3 |
| 1 | 2 | 3 |
\( \therefore \) LCM of 18, 36 and 27 = 3 x 3 x 2 x 2 x 3
= 108
In simple words: The Least Common Multiple (LCM) is the smallest positive integer that is divisible by each of the given integers. It is found by multiplying all unique prime factors raised to their highest powers from the prime factorization of each number.
🎯 Exam Tip: Students should practice the division method for finding LCM, ensuring all prime factors are accounted for, and present calculations clearly to avoid errors. This method is fundamental for solving problems involving common multiples.
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
Answer:
(i) 32, 37
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
\( \therefore \) 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
\( \therefore \) HCF x LCM = Product of the given numbers.
(ii) 46, 51
46 = 2 x 23 x 1
51 = 3 x 17 x 1
\( \therefore \) 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
\( \therefore \) HCF x LCM = Product of the given numbers.
(iii) 15, 60
15 = 3 x 5
60 = 2 x 30
= 2 x 2 x 15
= 2 x 2 x 3 x 5
\( \therefore \) 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
\( \therefore \) HCF x LCM = Product of the given numbers.
(iv) 18, 63
18 = 2 x 9
= 2 x 3 x 3
63 = 3 x 21
= 3 x 3 x 7
\( \therefore \) 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
\( \therefore \) HCF x LCM = Product of the given numbers.
(v) 78, 104
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
\( \therefore \) 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
\( \therefore \) HCF x LCM = Product of the given numbers.
In simple words: The HCF (Highest Common Factor) is the largest number that divides two or more numbers without leaving a remainder, while the LCM is the smallest common multiple. For any two positive integers, the product of their HCF and LCM is always equal to the product of the numbers themselves.
🎯 Exam Tip: Understanding the relationship HCF x LCM = Product of Numbers is crucial. Students should verify this property after calculating HCF and LCM, as it serves as an excellent check for accuracy in calculations involving two numbers.
Maharashtra Board Class 7 Maths Chapter 3 HCF And LCM Practice Set 13 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
Answer:
(i) Multiples of 6 : 6, 12, 18, 24, 30, 36, 42
Multiples of 7 : 7, 14, 21, 28, 35, 42, 49
\( \therefore \) LCM of 6 and 7 = 42
(ii) Multiples of 8 : 8, 16, 24, 32, 40
Multiples of 12 : 12, 24, 36, 48
\( \therefore \) 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
\( \therefore \) LCM of 5,6 and 15 = 30
In simple words: The Least Common Multiple (LCM) is the smallest number that appears in the list of multiples for all the given numbers. Listing out multiples helps visualize and identify this common multiple.
🎯 Exam Tip: For smaller numbers, listing multiples is a straightforward way to find the LCM. Ensure you list enough multiples to find the first common one, and double-check your arithmetic for each table to avoid errors.
MSBSHSE Solutions Class 7 Maths Chapter 3 Set 13 HCF and LCM
Students can now access the MSBSHSE Solutions for Chapter 3 Set 13 HCF and LCM prepared by teachers on our website. These solutions cover all questions in exercise in your Class 7 Maths textbook. Each answer is updated based on the current academic session as per the latest MSBSHSE syllabus.
Detailed Explanations for Chapter 3 Set 13 HCF and LCM
Our expert teachers have provided step-by-step explanations for all the difficult questions in the Class 7 Maths chapter. Along with the final answers, we have also explained the concept behind it to help you build stronger understanding of each topic. This will be really helpful for Class 7 students who want to understand both theoretical and practical questions. By studying these MSBSHSE Questions and Answers your basic concepts will improve a lot.
Benefits of using Maths Class 7 Solved Papers
Using our Maths solutions regularly students will be able to improve their logical thinking and problem-solving speed. These Class 7 solutions are a guide for self-study and homework assistance. Along with the chapter-wise solutions, you should also refer to our Revision Notes and Sample Papers for Chapter 3 Set 13 HCF and LCM to get a complete preparation experience.
FAQs
The complete and updated Maharashtra Board Class 7 Chapter 3 Set 13 HCF and LCM Solutions is available for free on StudiesToday.com. These solutions for Class 7 Maths are as per latest MSBSHSE curriculum.
Yes, our experts have revised the Maharashtra Board Class 7 Chapter 3 Set 13 HCF and LCM Solutions as per 2026 exam pattern. All textbook exercises have been solved and have added explanation about how the Maths concepts are applied in case-study and assertion-reasoning questions.
Toppers recommend using MSBSHSE language because MSBSHSE marking schemes are strictly based on textbook definitions. Our Maharashtra Board Class 7 Chapter 3 Set 13 HCF and LCM Solutions will help students to get full marks in the theory paper.
Yes, we provide bilingual support for Class 7 Maths. You can access Maharashtra Board Class 7 Chapter 3 Set 13 HCF and LCM Solutions in both English and Hindi medium.
Yes, you can download the entire Maharashtra Board Class 7 Chapter 3 Set 13 HCF and LCM Solutions in printable PDF format for offline study on any device.