CBSE Class 7 Maths Chapter 11: Finding Common Ground — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 11: Finding Common Ground from the NCERT Class 7 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): The HCF of two numbers is their greatest common factor.
Reason (R): It divides both numbers without remainder.
Reason (R): It divides both numbers without remainder.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The greatest shared divisor is selected.
2
Assertion (A): The HCF of 12 and 16 is 4.
Reason (R): The LCM of 3 and 4 is 12.
Reason (R): The LCM of 3 and 4 is 12.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the second does not explain the first.
3
Assertion (A): Their common factors include 1,2,3 and 6.
Reason (R): The HCF of 18 and 24 is 12.
Reason (R): The HCF of 18 and 24 is 12.
Answer: (c)
A is true, but R is false. The greatest common factor is 6.
4
Assertion (A): The HCF of two coprime numbers is 2.
Reason (R): Coprime numbers have HCF 1.
Reason (R): Coprime numbers have HCF 1.
Answer: (d)
A is false, but R is true. That is their defining property.
5
Assertion (A): The LCM is the least positive common multiple.
Reason (R): It is the first positive value appearing in both multiples lists.
Reason (R): It is the first positive value appearing in both multiples lists.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The least shared multiple is chosen.
6
Assertion (A): The LCM of 6 and 8 is 24.
Reason (R): The HCF of 6 and 8 is 2.
Reason (R): The HCF of 6 and 8 is 2.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the HCF value does not by itself explain the LCM list.
7
Assertion (A): Twenty is divisible by both 4 and 10.
Reason (R): The LCM of 4 and 10 is 40.
Reason (R): The LCM of 4 and 10 is 40.
Answer: (c)
A is true, but R is false. The least common multiple is 20.
8
Assertion (A): The LCM of a number and its multiple is their product.
Reason (R): The larger number itself is a common multiple.
Reason (R): The larger number itself is a common multiple.
Answer: (d)
A is false, but R is true. The LCM is the larger number.
9
Assertion (A): Prime factorisation can compute HCF by taking minimum common exponents.
Reason (R): Only prime factors shared by all numbers enter the HCF.
Reason (R): Only prime factors shared by all numbers enter the HCF.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Minimum exponents ensure divisibility into each number.
10
Assertion (A): LCM uses maximum prime exponents present.
Reason (R): Euclid's procedure can compute HCF by repeated remainders.
Reason (R): Euclid's procedure can compute HCF by repeated remainders.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true methods, but the HCF algorithm does not explain the LCM exponent rule.
11
Assertion (A): HCF uses the smaller exponent of each common prime.
Reason (R): The HCF of 2^3 x 3 and 2 x 3^2 is 2^3 x 3^2.
Reason (R): The HCF of 2^3 x 3 and 2 x 3^2 is 2^3 x 3^2.
Answer: (c)
A is true, but R is false. The HCF is 2 x 3 = 6.
12
Assertion (A): The LCM of 12 and 18 is 24.
Reason (R): Their prime factors require 2^2 x 3^2.
Reason (R): Their prime factors require 2^2 x 3^2.
Answer: (d)
A is false, but R is true. The LCM is 36.
13
Assertion (A): For two positive integers, HCF x LCM equals their product.
Reason (R): Prime exponents split into minimum and maximum values.
Reason (R): Prime exponents split into minimum and maximum values.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. For each prime, min plus max equals the exponent sum.
14
Assertion (A): HCF helps find the largest equal tile fitting two dimensions.
Reason (R): LCM helps find when repeating cycles next coincide.
Reason (R): LCM helps find when repeating cycles next coincide.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both applications are true, but cycle timing does not explain tiling.
15
Assertion (A): A common factor must divide both numbers.
Reason (R): A common factor of 20 and 30 can be 7.
Reason (R): A common factor of 20 and 30 can be 7.
Answer: (c)
A is true, but R is false. Seven divides neither exactly.
16
Assertion (A): A common multiple of 6 and 9 can be 20.
Reason (R): A common multiple must be divisible by both.
Reason (R): A common multiple must be divisible by both.
Answer: (d)
A is false, but R is true. Twenty is not divisible by either.
17
Assertion (A): Euclid's algorithm replaces a pair by the smaller number and the remainder.
Reason (R): This replacement preserves the HCF.
Reason (R): This replacement preserves the HCF.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Common divisors remain unchanged.
18
Assertion (A): Consecutive positive integers are coprime.
Reason (R): One of two consecutive integers may be even.
Reason (R): One of two consecutive integers may be even.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but parity does not explain all common factors.
19
Assertion (A): The smaller number is the greatest common divisor.
Reason (R): If one number divides another, their HCF is the larger number.
Reason (R): If one number divides another, their HCF is the larger number.
Answer: (c)
A is true, but R is false. The HCF is the divisor, namely the smaller number.
20
Assertion (A): The LCM is always smaller than both positive numbers.
Reason (R): The LCM is at least as large as each number.
Reason (R): The LCM is at least as large as each number.
Answer: (d)
A is false, but R is true. It must be a multiple of both.
❓ Frequently Asked Questions
What is covered in CBSE Class 7 Maths Chapter 11 Finding Common Ground?
This chapter covers all key topics from Finding Common Ground as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 7 board exam preparation covering the complete syllabus.
Are these CBSE Class 7 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 7 Maths?
All chapters of CBSE Class 7 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study Finding Common Ground online for free?
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