Chapter-11 Finding Common Ground — Online MCQ Test
MATHS · Grade 7 · CBSE(NCERT)
Practice Chapter-11 Finding Common Ground with a free chapter-wise online MCQ test.
This chapter covers: HCF - LCM - optimization - factors - multiples.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter-11 Finding Common Ground — Important Questions & Answers
What is the full form of HCF?
- A. Highest Common Factor
- B. Highest Common Figure
- C. High Calculation Formula
- D. Horizontal Common Factor
Answer: A. Highest Common Factor
HCF stands for Highest Common Factor, which is the largest number that divides two or more numbers without leaving a remainder.
HCF stands for Highest Common Factor, which is the largest number that divides two or more numbers without leaving a remainder.
What is the full form of LCM?
- A. Least Common Multiple
- B. Large Common Multiple
- C. Lowest Calculation Method
- D. Least Common Measure
Answer: A. Least Common Multiple
LCM stands for Least Common Multiple, which is the smallest number that is a multiple of two or more given numbers.
LCM stands for Least Common Multiple, which is the smallest number that is a multiple of two or more given numbers.
Which of the following is a factor of 24?
- A. 5
- B. 7
- C. 8
- D. 11
Answer: C. 8
A factor of 24 is a number that divides 24 completely. 24 ÷ 8 = 3, so 8 is a factor of 24.
A factor of 24 is a number that divides 24 completely. 24 ÷ 8 = 3, so 8 is a factor of 24.
Which of the following is a multiple of 6?
- A. 16
- B. 24
- C. 25
- D. 35
Answer: B. 24
A multiple of 6 is obtained by multiplying 6 by a whole number. 6 × 4 = 24, so 24 is a multiple of 6.
A multiple of 6 is obtained by multiplying 6 by a whole number. 6 × 4 = 24, so 24 is a multiple of 6.
Find the HCF of 15 and 25 using prime factorization.
- A. 3
- B. 5
- C. 15
- D. 75
Answer: B. 5
15 = 3 × 5 and 25 = 5 × 5. The common prime factor is 5, so HCF = 5.
15 = 3 × 5 and 25 = 5 × 5. The common prime factor is 5, so HCF = 5.
Find the LCM of 8 and 12 using prime factorization.
- A. 24
- B. 48
- C. 96
- D. 20
Answer: A. 24
8 = 2³ and 12 = 2² × 3. LCM = 2³ × 3 = 8 × 3 = 24.
8 = 2³ and 12 = 2² × 3. LCM = 2³ × 3 = 8 × 3 = 24.
Compare: HCF(12, 18) ___ HCF(15, 25)
- A. Greater than
- B. Less than
- C. Equal to
- D. Cannot be determined
Answer: A. Greater than
HCF(12, 18) = 6 and HCF(15, 25) = 5. Since 6 > 5, HCF(12, 18) is greater than HCF(15, 25).
HCF(12, 18) = 6 and HCF(15, 25) = 5. Since 6 > 5, HCF(12, 18) is greater than HCF(15, 25).
The HCF of two consecutive even numbers is always ___.
- A. 1
- B. 2
- C. 4
- D. Depends on the numbers
Answer: B. 2
Consecutive even numbers like 4 and 6, or 8 and 10, always have HCF = 2 because they share only 2 as a common factor.
Consecutive even numbers like 4 and 6, or 8 and 10, always have HCF = 2 because they share only 2 as a common factor.
The factors of 28 are 1, 2, 4, 7, 14, 28. The sum of all factors is ___.
- A. 56
- B. 42
- C. 48
- D. 112
Answer: A. 56
Sum = 1 + 2 + 4 + 7 + 14 + 28 = 56. This is a direct calculation of the sum of all factors.
Sum = 1 + 2 + 4 + 7 + 14 + 28 = 56. This is a direct calculation of the sum of all factors.
Which set of numbers has LCM = 60 and HCF = 6?
- A. 6, 12, 30
- B. 12, 20, 30
- C. 6, 12, 60
- D. 10, 12, 60
Answer: C. 6, 12, 60
For 6, 12, 60: Factors of 6={1,2,3,6}, 12={1,2,3,4,6,12}, 60={1,2,3,4,5,6,10,12,15,20,30,60}. HCF=6, LCM=60. This is correct.
For 6, 12, 60: Factors of 6={1,2,3,6}, 12={1,2,3,4,6,12}, 60={1,2,3,4,5,6,10,12,15,20,30,60}. HCF=6, LCM=60. This is correct.