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NMAT HCF and LCM — practice questions

Explore 29 free HCF and LCM questions in NMAT Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.

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HCF and LCM questions and exercises with answers

Showing questions 1–29 of 29.

The largest positive integer that divides both of two numbers is their:Read the answer and worked solution →The algorithm that finds that largest common divisor by repeated division is named after:Read the answer and worked solution →Using that algorithm on 455 and 42, the first step gives 455 = 42 times 10 plus:Read the answer and worked solution →Continuing, 42 = 35 times 1 plus 7, then 35 = 7 times 5 plus 0. The largest common divisor is:Read the answer and worked solution →The theorem saying every composite number can be written as a product of primes is the:Read the answer and worked solution →Writing 20 as 2 times 2 times 5 is an example of:Read the answer and worked solution →The highest common factor of 6 and 20 is:Read the answer and worked solution →The lowest common multiple of 6 and 20 is:Read the answer and worked solution →The highest common factor is found by taking, for each common prime, the:Read the answer and worked solution →The lowest common multiple is found by taking, for each prime involved, the:Read the answer and worked solution →For any two positive integers, the product of their highest common factor and lowest common multiple equals:Read the answer and worked solution →The prime factorisation of 96 gives a highest common factor with 404 of:Read the answer and worked solution →Using that result, the lowest common multiple of 96 and 404 is:Read the answer and worked solution →The highest common factor of 6, 72 and 120 is:Read the answer and worked solution →The lowest common multiple of 6, 72 and 120 is:Read the answer and worked solution →For three numbers, the product of the numbers is:Read the answer and worked solution →Knowing the highest common factor of two numbers lets you find their lowest common multiple by:Read the answer and worked solution →If two numbers share no prime factor at all, their highest common factor must be:Read the answer and worked solution →A number like root 2, which cannot be written as a ratio of integers, is described as:Read the answer and worked solution →If a prime p divides the square of a number a, the theorem states that p also divides:Read the answer and worked solution →The two main tools introduced for studying real numbers here are prime factorisation and:Read the answer and worked solution →Catch the prime factorsRead the answer and worked solution →Pop the correct answersRead the answer and worked solution →Run the factor gatesRead the answer and worked solution →Slice the number wordsRead the answer and worked solution →Smallest or greatest powerRead the answer and worked solution →Sort the resultsRead the answer and worked solution →Type the numberRead the answer and worked solution →Number theory bingoRead the answer and worked solution →

Worked practice questions

The largest positive integer that divides both of two numbers is their:

  1. Highest common factor
  2. Highest common fraction
  3. Highest common fragment
  4. Highest common formula
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Correct answer: A. Highest common factor

1. It must divide both numbers exactly. 2. Among such divisors it is the largest. 3. It is the highest common factor. _Source: syllabus Mathematics, Chapter 1, Real Numbers._

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The algorithm that finds that largest common divisor by repeated division is named after:

  1. Ehrlich
  2. Euclid
  3. Euler
  4. Edison
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Correct answer: B. Euclid

1. A division lemma drives it. 2. Divisor and remainder are used again and again. 3. It is Euclid's algorithm. _Source: syllabus Mathematics, Chapter 1, Real Numbers._

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Using that algorithm on 455 and 42, the first step gives 455 = 42 times 10 plus:

  1. 35
  2. 25
  3. 45
  4. 15
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Correct answer: A. 35

1. Ten forty-twos make 420. 2. 455 minus 420 leaves the remainder. 3. The remainder is 35. _Source: syllabus Mathematics, Chapter 1, Real Numbers._

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