CAT Practice : Number System: HCF, LCM

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The following topics are covered in the CAT quant section from Number system - HCF, LCM. Detailed explanatory answers, solution videos and slide decks are also provided.
  1. Number Theory - HCF LCM

    How many pairs of integers (x, y) exist such that the product of x, y and HCF (x, y) = 1080?

    1. 8
    2. 7
    3. 9
    4. 12
  2. Number Theory - Remainders LCM

    Find the smallest number that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9?

    1. 2519
    2. 5039
    3. 1079
    4. 979
  3. HCF LCM - Theory

    There are three numbers a,b, c such that HCF (a, b) = l, HCF (b, c) = m and HCF (c, a) = n. HCF (l, m) = HCF (l, n) = HCF (n, m) = 1. Find LCM of a, b, c. (The answer can be "This cannot be determined").

    • Correct AnswerCannot be determined Correct answer
    • Explanatory Answer
    • HCF LCM, tough algebraic qn
    • Hard
  4. HCF basics

    How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?

    1. 12
    2. 8
    3. 15
    4. 30
  5. HCF LCM

    How many pairs of positive integers x, y exist such that HCF (x, y) + LCM (x, y) = 91?

    1. 10
    2. 8
    3. 6
    4. 7
  6. HCF basics

    Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?

    1. 350
    2. 700
    3. 1050
    4. 525
  7. HCF basics

    The sum of two non co–prime numbers added to their HCF gives us 91. How many such pairs are possible?

    1. 2
    2. 4
    3. 3
    4. 6
  8. HCF LCM basics

    There are 2 numbers such that a > b, HCF (a, b) = h and LCM (a, b) = l. What is the LCM of a – b and b?

    1. l
    2. (a - b) b
    3. (a - b) b / h
    4. h (a - b)
    • Correct AnswerChoice (C).
      (a - b) b / h
      Correct answer
    • Explanatory Answer
    • HCF LCM basics
    • Medium
  9. No of sweet boxes

    6 different sweet varieties of count 32, 216, 136, 88, 184, 120 were ordered for a particular occasion. They need to be packed in such a way that each box has the same variety of sweet and the number of sweets in each box is also the same. What is the minimum number of boxes required to pack?

    1. 129
    2. 64
    3. 48
    4. 97

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