Shortcut Of LCM And HCF Quiz

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| By Gregorynaomi

Gregorynaomi

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Quizzes Created: 1463 | Total Attempts: 755,840

Questions: 10 | Attempts: 650 | Updated: Mar 20, 2023

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LCM and HCF are concepts useful in mathematics as well as in determining the time and distance, pipes and cisterns and so on. There are many shortcuts and tricks in analyzing the concepts problems which requires some principles and methods for easy calculations. Co-prime numbers, Prime numbers and terms like multiples, factors and so on are required for easy use of the shortcuts.

Questions and Answers

1.

What is the least common multiple of 3 and 4?
- A.
  
  24
- B.
  
  12
- C.
  
  48
- D.
  
  36
Correct Answer
B. 12

Explanation
The least common multiple (LCM) is the smallest number that is divisible by both 3 and 4 without leaving a remainder. To find the LCM, we can list the multiples of both numbers and find the smallest common multiple. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, ... and the multiples of 4 are 4, 8, 12, 16, 20, 24, ... The smallest common multiple is 12, which means it is the least common multiple of 3 and 4.

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2.

What is the integral values of number that can provide the number?
- A.
  
  Prime numbers
- B.
  
  LCM
- C.
  
  HCF
- D.
  
  Prime Factors
Correct Answer
C. HCF

Explanation
The correct answer is HCF. HCF stands for Highest Common Factor, which is the largest number that divides two or more numbers without leaving a remainder. The integral values of a number that can provide the number would be the factors of that number, and the HCF represents the common factors among those numbers. Therefore, the HCF is the correct answer for this question.

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3.

Which of these always divides the LCM of a number?
- A.
  
  10
- B.
  
  Prime Factors
- C.
  
  HCF
- D.
  
  LCF
Correct Answer
C. HCF

Explanation
The highest common factor (HCF) always divides the least common multiple (LCM) of a number. This is because the LCM is the smallest multiple that is divisible by all the given numbers, and the HCF is the largest number that divides all the given numbers. Therefore, the HCF must also divide the LCM.

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1
0
4.

Which of these is the multiple of 3 and 5?
- A.
  
  15
- B.
  
  10
- C.
  
  12
- D.
  
  14
Correct Answer
A. 15

Explanation
15 is the correct answer because it is divisible by both 3 and 5. When 15 is divided by 3, the remainder is 0 because 15 is a multiple of 3. Similarly, when 15 is divided by 5, the remainder is also 0 because 15 is a multiple of 5. Therefore, 15 satisfies the condition of being a multiple of both 3 and 5.

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1
0
5.

What is the other name for HCF?
- A.
  
  LCF
- B.
  
  GCF
- C.
  
  HCM
- D.
  
  PCM
Correct Answer
B. GCF

Explanation
The other name for HCF is GCF, which stands for Greatest Common Factor. HCF and GCF are interchangeable terms used to refer to the largest number that divides two or more given numbers without leaving a remainder.

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1
0
6.

What is the name given to number having many factors?
- A.
  
  Even number
- B.
  
  Odd number
- C.
  
  Composite number
- D.
  
  Prime number
Correct Answer
C. Composite number

Explanation
A composite number is a number that has more than two factors. It is not a prime number, which only has two factors (1 and itself). Composite numbers can be divided evenly by at least one other number besides 1 and itself. Therefore, the name given to a number having many factors is a composite number.

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7.

What is the product of common prime factors in respect to highest indices?
- A.
  
  1
- B.
  
  GCF
- C.
  
  HCF
- D.
  
  LCM
Correct Answer
C. HCF

Explanation
The product of common prime factors in respect to highest indices refers to finding the highest power of each prime number that appears in all the given numbers. The highest common factor (HCF) is the product of these prime factors. Therefore, the correct answer is HCF.

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8.

What is the common multiple of 2,3,6 and 9?
- A.
  
  9
- B.
  
  16
- C.
  
  18
- D.
  
  20
Correct Answer
C. 18

Explanation
The common multiple of 2, 3, 6, and 9 is 18 because it is the smallest number that is divisible by all of these numbers without leaving a remainder.

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9.

Which of these is not a prime number?
- A.
  
  3
- B.
  
  5
- C.
  
  17
- D.
  
  4
Correct Answer
D. 4

Explanation
A prime number is a number that is only divisible by 1 and itself. 3, 5, and 17 are all prime numbers because they can only be divided by 1 and themselves. However, 4 is not a prime number because it can be divided by 1, 2, and 4. Therefore, 4 is the correct answer as it is not a prime number.

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10.

Which of these numbers are said to be co-primes?
- A.
  
  1 and 2
- B.
  
  1 and 4
- C.
  
  2 and 3
- D.
  
  6 and 7
Correct Answer
D. 6 and 7

Explanation
Co-primes are numbers that have only 1 as their common factor. In this case, 6 and 7 are said to be co-primes because they do not have any common factors other than 1.

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