Class 7 Maths Ganita Prakash Part 2 Chapter 3 MCQs – Finding Common Ground

Use these Finding Common Ground Class 7 MCQ questions to revise the Highest Common Factor (HCF) and Lowest Common Multiple (LCM). Finding Common Ground is Chapter 3 of Class 7 Maths Ganita Prakash Part 2 and it links them to everyday problems, such as choosing the largest square tile for a floor. The questions test prime factorisation by the division method, finding the HCF and LCM, patterns with co-prime, consecutive numbers and the rule HCF × LCM = product of the two numbers.

Finding Common Ground Class 7 MCQ Questions with Answers

Class 7 Maths Part 2 Chapter 3 MCQs Set 1

Q1. A 12 ft by 16 ft floor is to be covered by identical square tiles in rows, without gaps, overlaps or cutting. If each tile’s side is a whole number of feet, what is the largest possible side length?

[A]. 2 ft
[B]. 4 ft
[C]. 12 ft
[D]. 8 ft

Q2. How many square tiles of side 4 ft cover a 12 ft by 16 ft floor without gaps or overlaps?

[A]. 16
[B]. 48
[C]. 12
[D]. 7

Q3. Rice amounts of 84 kg and 108 kg must be packed separately into bags of equal whole-number weight, with none left over. What bag weight gives the fewest bags?

[A]. 6 kg
[B]. 36 kg
[C]. 12 kg
[D]. 24 kg

Q4. Rice from two farms weighs 84 kg and 108 kg. It is packed in 12 kg bags, keeping the farms’ rice separate. How many bags are needed altogether?

[A]. 12
[B]. 192
[C]. 18
[D]. 16

Q5. Jumpy starts at 0 and makes equal whole-number jumps along a number line. What is the longest jump that lets Jumpy land on both 28 and 42?

[A]. 7 units
[B]. 21 units
[C]. 28 units
[D]. 14 units

Class 7 Maths Part 2 Chapter 3 MCQs Set 2

Q6. Which expression is the prime factorisation of 90?

[A]. 2 × 45
[B]. 3 × 30
[C]. 2 × 3 × 3 × 5
[D]. 9 × 10

Q7. Given 840 = 2 × 2 × 2 × 3 × 5 × 7, which number is NOT a factor of 840?

[A]. 8
[B]. 27
[C]. 28
[D]. 14

Q8. The positive factors of 225 are formed from 225 = 3 × 3 × 5 × 5. How many distinct positive factors does 225 have?

[A]. 8
[B]. 10
[C]. 9
[D]. 4

Q9. Anshu claims that every larger number has more prime factors when repetitions are counted. Which fact disproves this claim?

[A]. 105 = 3 × 5 × 7.
[B]. 90 = 2 × 3 × 3 × 5.
[C]. 96 has six prime factors with repetition, while the larger 121 has only two.
[D]. A prime number is greater than 1.

Q10. What is the HCF of 45 and 75?

[A]. 5
[B]. 3
[C]. 15
[D]. 225

Class 7 Maths Part 2 Chapter 3 MCQs Set 3

Q11. What is the HCF of 112 and 84?

[A]. 7
[B]. 56
[C]. 14
[D]. 28

Q12. Given 96 = 2 × 2 × 2 × 2 × 2 × 3 and 275 = 5 × 5 × 11, what is their HCF?

[A]. 2
[B]. 11
[C]. 5
[D]. 1

Q13. What is the HCF of 225 and 750?

[A]. 25
[B]. 15
[C]. 150
[D]. 7

Q14. What is the HCF of 42, 75 and 24?

[A]. 2
[B]. 3
[C]. 15
[D]. 6

Q15. A student writes 72 = 6 × 12 and 144 = 8 × 18, then claims that 72 and 144 have no common factor except 1. What is their actual HCF?

[A]. 6
[B]. 72
[C]. 1
[D]. 12

Class 7 Maths Part 2 Chapter 3 MCQs Set 4

Q16. Anshu joins 6 cm strips end to end, and Guna joins 8 cm strips end to end. What is the shortest positive length they can both make without cutting strips?

[A]. 24 cm
[B]. 14 cm
[C]. 48 cm
[D]. 2 cm

Q17. Kabamai visits a shop every 10 days. Free sweets are given every Monday, and she visits on a Monday today. After how many days will her next visit fall on a Monday?

[A]. 70 days
[B]. 10 days
[C]. 17 days
[D]. 35 days

Q18. What is the LCM of 14 and 35?

[A]. 70
[B]. 49
[C]. 7
[D]. 490

Q19. What is the LCM of 96 and 360?

[A]. 2880
[B]. 1440
[C]. 24
[D]. 720

Q20. What is the LCM of 105, 195 and 65?

[A]. 195
[B]. 65
[C]. 4095
[D]. 1365

Class 7 Maths Part 2 Chapter 3 MCQs Set 5

Q21. What is the HCF of any two consecutive positive even numbers?

[A]. 2
[B]. The smaller number in every case
[C]. 4
[D]. 1

Q22. The HCF of 270 and 50 is 10. What is the HCF of 540 and 100?

[A]. 20
[B]. 10
[C]. 40
[D]. 100

Q23. What is the HCF of 14 × 6 and 14 × 9?

[A]. 42
[B]. 14
[C]. 126
[D]. 6

Q24. For positive integers a and b, which relation is always correct?

[A]. HCF(a, b) = a × b
[B]. HCF(a, b) + LCM(a, b) = a + b
[C]. LCM(a, b) = a + b
[D]. HCF(a, b) × LCM(a, b) = a × b

Q25. The HCF of 630 and 770 is 70. What is their LCM?

[A]. 70
[B]. 700
[C]. 6930
[D]. 53900

Class 7 Maths Part 2 Chapter 3 MCQs Set 6

Q26. A cowherd has a positive number of cows, fewer than 200. The cows can form equal groups through 3 gates, 5 gates or 7 gates, with none left over. How many cows are there?

[A]. 35
[B]. 105
[C]. 210
[D]. 150

Q27. A box measures 12 cm × 18 cm × 36 cm. What is the largest whole-number side length of identical cubes that can fill it in rows without gaps?

[A]. 18 cm
[B]. 12 cm
[C]. 6 cm
[D]. 9 cm

Q28. What is the smallest positive number divisible by 3, 4, 5 and 7 that leaves remainder 10 when divided by 11?

[A]. 840
[B]. 2100
[C]. 1680
[D]. 420

Q29. A rabbit is 150 ft ahead of a dog. For every jump of 7 ft by the rabbit, the dog makes one jump of 9 ft. After how many such pairs of jumps does the dog catch the rabbit?

[A]. 75
[B]. 150
[C]. 50
[D]. 17

Q30. What is 8/15 + 1/20 + 7/36 + 11/63 + 1/21?

[A]. 1
[B]. 5/6
[C]. 1/2
[D]. 2

Go Beyond the MCQs on HCF and LCM

Many Finding Common Ground MCQs can be checked quickly with patterns from the chapter. Two consecutive numbers always have an HCF of 1, so their LCM is simply their product, and the same holds for any pair of co-prime numbers. When one number is a factor of the other, the smaller number is the HCF and the larger one is the LCM. Use these shortcuts to rule out options, but confirm with prime factorisation when the numbers are large. HCF and LCM also help you reduce fractions to lowest terms and add fractions with unlike denominators, so pair this chapter with Working with Fractions from Part 1 on the Class 7 Maths MCQ page. Where both parts are numbered together, this appears as Chapter 11.

Ganita Prakash Part 2 Chapter 3 asks for more than final answers. Several Figure it Out questions ask you to make a general statement, such as describing the HCF of two consecutive even numbers, and then explain why it is always true. The chapter calls this generalisation and uses the word conjecture for a claim made without proof, which a single counterexample can disprove. The NCERT Solutions for Class 7 Maths show how to test such statements with examples and justify them, along with full working for word problems on tiles, torans and repeating events, like a weekly offer and a visit every 10 days. Attempt each question yourself before reading the solution.