LCM and HCF


  1. The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets same number of pens and same number of pencils, is :









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    As we know that ,
    Maximum number of students = The greatest common divisor = HCF of 1001 and 910

    Correct Option: A

    As we know that ,
    Maximum number of students = The greatest common divisor = HCF of 1001 and 910 = 91


  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









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









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    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. 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?









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    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. Three bells ring at intervals of 36 seconds, 40 seconds and 48 seconds respectively. They start ringing together at a particular time. They will ring together after every









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    Required answer = LCM of 36, 40 and 48 seconds

    ∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720

    Correct Option: B

    Required answer = LCM of 36, 40 and 48 seconds
    = 720 seconds

    Required answer =
    720
    minutes = 12 minutes
    60


    ∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720