LCM and HCF

LCM and HCF

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Aptitude miscellaneous
  1. Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time do they meet at the starting point for the first time ?








  1. View Hint View Answer Discuss in Forum

    Required time = LCM of 200, 300, 360 and 450 seconds
    We find , LCM of 200, 300, 360 and 450 seconds = 1800 seconds

    Correct Option: A

    Required time = LCM of 200, 300, 360 and 450 seconds
    We find , LCM of 200, 300, 360 and 450 seconds = 1800 seconds
    ∴ Required time = 1800 seconds

  1. Five bells begin to toll together and toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. After how many seconds will they toll together again ?








  1. View Hint View Answer Discuss in Forum

    Required time = LCM of 6, 7, 8, 9 and 12 seconds = 504 seconds

    Correct Option: C

    Required time = LCM of 6, 7, 8, 9 and 12 seconds = 504 seconds

  1. The greatest number of four digits which when divided by 3, 5, 7, 9 leave remainders 1, 3, 5, 7 respectively is :








  1. View Hint View Answer Discuss in Forum

    The difference between divisor and the corresponding remainder is equal.
    LCM of 3, 5, 7 and 9 = 315
    Largest 4-digit number = 9999

    ∴ Number divisible by 315 = 9999 – 234 = 9765

    Correct Option: A

    The difference between divisor and the corresponding remainder is equal.
    LCM of 3, 5, 7 and 9 = 315
    Largest 4-digit number = 9999

    ∴ Number divisible by 315 = 9999 – 234 = 9765
    Required number = 9765 – 2 = 9763

  1. Three bells ring simultaneously at 11a.m. They ring at regular intervals of 20 minutes, 30 minutes, 40 minutes respectively. The time when all the three ring together next is








  1. View Hint View Answer Discuss in Forum

    LCM of 20, 30 and 40 minutes = 120 minutes
    Hence, the bells will toll together again after 2 hours i.e. at 1 p.m.

    Correct Option: B

    LCM of 20, 30 and 40 minutes = 120 minutes
    Hence, the bells will toll together again after 2 hours i.e. at 1 p.m.
    Required time = 1 p.m.

  1. L.C.M. of
    2
    		,
    4
    		,
    5
    		is
    3 9 6








  1. View Hint View Answer Discuss in Forum

    As we know that ,

    LCM of fractions =
    LCM of numerators
    HCF of denominators

    LCM =
    LCM of 2, 4, 5
    HCF of 3, 9, 6

    Correct Option: B

    As we know that ,

    LCM of fractions =
    LCM of numerators
    HCF of denominators

    LCM =
    LCM of 2, 4, 5
    HCF of 3, 9, 6

    LCM =
    20
    3