Explore numerous Class 7 Maths MCQ and Ganita Prakash Class 7 Maths Part 2 Chapter 3 Finding Common Ground MCQ Online Test with Answers provided with detailed solutions by looking below.
MCQ on Finding Common Ground Class 7
Finding Common Ground Class MCQ Class 7
Class 7 Finding Common Ground Class MCQ
Question 1.
A person claps on multiples of 4 and snaps on multiples of 6. When do they do both simultaneously?
(a) 4, 6, 8
(b) 12, 24, 36
(c) 10, 20, 30
(d) 4, 12, 24
Solution:
(b) 12, 24, 36 (Multiples of LCM 12)
Question 2.
What is the HCF of 45 and 75 ?
(a) 5
(b) 10
(c) 15
(d) 25
Solution:
(c) 15 (Prime factorization: 45=3 × 3 × 5, 75 =3 × 5 × 5 )
Question 3.
What is the prime factorization of 225?
(a) 3 ×5 ×15
(b) 3 × 3 × 5 × 5
(c) 5 × 5 × 9
(d) 3 × 5 × 5 × 5
Solution:
(b) 3 × 3 × 5 × 5
Question 4.
Which of the following numbers are coprime?
(a) 10 and 21
(b) 12 and 15
(c) 14 and 21
(d) 9 and 27
Solution:
(a) 10 and 21 (They have no common factor other than 1)
Question 5.
A number is divisible by 12. What other numbers must it be divisible by?
(a) 3 and 4
(b) 5 and 6
(c) 7 and 2
(d) 8 and 3
Solution:
(a) 3 and 4 (Factors of 12)
Question 6.
Arjun sets two alarms: one rings every 9 minutes and the other every 12 minutes. If they start together at 8:00 AM, at what time will they ring together again?
(a) 8:18 AM
(b) 8:24 AM
(c) 8:36 AM
(d) 9:00 AM
Solution:
(c) 8:36 AM
Explanation: To find why they ring together calculate the LCM of 9 and 12
Prime factorization: 9=3², 1²=2² × 3
LCM=2² × 3²=4 × 9 = 36 minutes
Adding to 8:00 AM gives 8:36 AM
Question 7.
Which of the following is the HCF of any two co-prime numbers?
(a) 0
(b) 1
(c) The product of the numbers
(d) The sum of the numbers
Solution:
(b) 1
Explanation: Co-prime numbers are defined as numbers that have no common prime factors, meaning their only common factor is 1.
Question 8.
HCF of 18 and 32 is: ……….
(a) 2
(b) 4
(c) 10
(d) 20
Solution:
(a) 2
Question 9.
LCM of 15, 20 and 25 is: ………..
(a) 80
(b) 60
(c) 100
(d) 120
Solution:
(c) 100
Question 10.
LCM of 8, 12 and 18 is: ………
(a) 52
(b) 72
(c) 62
(d) 82
Solution:
(b) 72
Question 11.
LCM of 18 and 24 is: …………..
(a) 24
(b) 12
(c) 72
(d) 14
Solution:
(c) 72
Question 12.
LCM of 9, 18 and 36 is: ………….
(a) 180
(b) 26
(c) 46
(d) 36
Solution:
(d) 36
Question 13.
Two tankers contain 850 L and 680 L of kerosene oil. Then the maximum capacity of container using both tankers at a time to fill it is:
(a) 170
(b) 160
(c) 180
(d) 240
Solution:
(a) 170
Question 14.
Which of the following is not a multiple of ‘6’?
(a) 36
(b) 60
(c) 70
(d) 66
Solution:
(c) 70
Question 15.
Find the LCM of 14 and 21.
(a) 34
(b) 60
(c) 56
(d) 42
Solution:
(d) 42
Question 16.
Find the LCM of 27, 36 and 45.
(a) 524
(b) 540
(c) 532
(d) 536
Solution:
(b) 540
Question 17.
Find the LCM of 16 and 24.
(a) 48
(b) 30
(c) 42
(d) 46
Solution:
(a) 48
Question 18.
Find the LCM of 54 and 72.
(a) 220
(b) 226
(c) 216
(d) 234
Solution:
(c) 216
Question 19.
Find the LCM of 8, 12 and 20.
(a) 118
(b) 120
(c) 126
(d) 106
Solution:
(b) 120
Question 20.
Find the LCM of 63 and 84.
(a) 260
(b) 256
(c) 204
(d) 252
Solution:
(d) 252
Question 21.
Find the LCM of 30 and 45.
(a) 86
(b) 90
(c) 44
(d) 24
Solution:
(b) 90
Question 22.
Find the LCM of 18, 24 and 36.
(a) 72
(b) 80
(c) 54
(d) 46
Solution:
(a) 72
Question 23.
Find the LCM of 42 and 56.
(a) 144
(b) 150
(c) 124
(d) 168
Solution:
(d) 168
Question 24.
Find the LCM of 15, 25 and 35.
(a) 546
(b) 564
(c) 525
(d) 534
Solution:
(c) 525
Question 25.
What is the HCF of 72 and 90?
(a) 9
(b) 12
(c) 18
(d) 36
Solution:
(c) 18
Question 26.
Find the HCF of 64 and 128.
(a) 16
(b) 32
(c) 64
(d) 128
Solution:
(c) 64
Question 27.
What is the HCF of 15 and 28?
(a) 1
(b) 3
(c) 5
(d) 7
Solution:
(a) 1 (They are co-prime)
Question 28.
Find the HCF of 24 and 36.
(a) 4
(b) 6
(c) 8
(d) 12
Solution:
(d) 12
Finding Common Ground Class 7 Assertion and Reason Questions
Instructions:
In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
(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.
Question 1.
Assertion (A) : The HCF of 12 and 18 is 6.
Reason (R) : The HCF of two or more given numbers is the largest common factor among them.
Analysis:
- A is True (Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors: 1, 2, 3, 6. Highest is 6).
- R is True (This is the definition of HCF).
- R explains A (The definition helps confirm the value 6 is the highest common factor).
Solution:
(a) Both A and R are true, and R is the correct explanation of A.
Question 2.
Assertion (A): The LCM of 7 and 11 is 77.
Reason (R): 7 and 11 are prime numbers, and the LCM of two prime numbers is their product.
Analysis :
- A is True (LCM of 7 and 11 is 77).
- R is True (The rule for prime numbers’ LCM is their product).
- R explains A (The reason justifies why the answer is 77).
Solution:
(a) Both A and R are true, and R is the correct explanation of A.
Question 3.
Assertion (A): The number 4 is a common factor of 8, 16, and 24.
Reason (R): The number 16 is a multiple of 8.
Analysis :
- A is True (4 divides 8, 16, and 24 evenly).
- R is True (16 = 8 × 2).
- R does not explain A (The reason talks about a multiple of two of the numbers, not why 4 is a common factor of all three).
Solution:
(b) Both A and R are true but R is not the correct explanation of A.
Finding Common Ground Class 7 Fill in the blanks
Question 1.
A number is a ………… of each of its factor.
Answer:
multiple
Question 2.
………… is a factor of every number.
Answer:
1
Question 3.
The number of factors of a prime number is
Answer:
2, 4
Question 4.
A number for which the sum of all its factors is equal to twice the number is called a ………… number.
Answer:
perfect
Question 5.
The numbers having more than two factors are called ………… numbers.
Answer:
composite
Question 6.
2 is the only ………… number which is even.
Answer:
prime
Question 7.
Two numbers having only 1 as a common factor are called ………… numbers.
Answer:
co-prime
Finding Common Ground Class 7 True or False
Question 1.
The Highest Common Factor of two or more numbers is greater than their Lowest Common Multiple.
Answer:
False
Question 2.
LCM of two or more numbers is divisible by their HCF.
Answer:
True
Question 3.
LCM of two numbers is 28 and their HCF is 8.
Answer:
False
Question 4.
LCM of two or more numbers may be one of the numbers.
Answer:
True
Question 5.
HCF of two or more numbers may be one of the numbers.
Answer:
True