LCM and HCF

LCM and HCF

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Aptitude miscellaneous
  1. The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to the fourth number. What is the sum of four numbers?








  1. View Hint View Answer Discuss in Forum

    We find LCM of 60 ,

    ∴ 60 = 2 × 2 × 3 × 5
    i.e., Numbers = 2, 3, 4 and 5

    Correct Option: B

    We find LCM of 60 ,

    ∴ 60 = 2 × 2 × 3 × 5
    i.e., Numbers = 2, 3, 4 and 5
    ∴ Required sum = 2 + 3 + 4 + 5 = 14

  1. The LCM fo two prime numbers p and q, (p > q) is 161. The value of (3q – p) :








  1. View Hint View Answer Discuss in Forum

    LCM of p and q = 161
    ∴ pq = 23 × 7
    ∴ p = 23; q = 7
    ∴ 3q – p = 3 × 7 – 23

    Correct Option: A

    LCM of p and q = 161
    ∴ pq = 23 × 7
    ∴ p = 23; q = 7
    ∴ 3q – p = 3 × 7 – 23
    The value of (3q – p) = 21 – 23 = – 2

  1. Three electronic devices make a beep after every 48 seconds, 72 seconds and 108 seconds respectively. They beeped together at 10 a.m. The time when they will next make a beep together at the earliest is








  1. View Hint View Answer Discuss in Forum

    Required time = LCM of 48, 72 and 108 seconds

    ∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432 seconds = 7 minutes 12 second

    Correct Option: A

    Required time = LCM of 48, 72 and 108 seconds

    ∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432 seconds = 7 minutes 12 second
    ∴ Required time = 10 a.m. + 7 minutes 12 second = 10 : 07 : 12 hours

  1. Three tankers contain 403 litres, 434 litres, 465 litres of diesel respectively. Then the maximum capacity of a container that can measure the diesel of the three containers exact number of times is








  1. View Hint View Answer Discuss in Forum

    Greatest capacity of measuring vessel
    = HCF of 403 litres, 434 litres and 465 litres
    First of all we find HCF of 403 and 434

    Again , HCF of 31 and 465

    Correct Option: A

    Greatest capacity of measuring vessel
    = HCF of 403 litres, 434 litres and 465 litres
    First of all we find HCF of 403 and 434

    Again , HCF of 31 and 465

    ∴ Greatest capacity of measuring vessel = 31 litres

  1. The greatest number that will divide 729 and 901 leaving remainders 9 and 5 respectively, is








  1. View Hint View Answer Discuss in Forum

    We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
    Required number = HCF of (729 – 9) = 720 and (901 – 5) = 896

    H.C.F = 16

    Correct Option: B

    We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
    Required number = HCF of (729 – 9) = 720 and (901 – 5) = 896

    H.C.F = 16
    Hence , required answer = 16.