LCM and HCF


  1. Find the least number which when divided by 12, 15, 20 and 24 leaves the same remainder 2 in each case ?









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    Required number = LCM of (12, 15, 20, 24) + 2

    Correct Option: A

    Required number = LCM of (12, 15, 20, 24) + 2
    = 120 + 2 = 122


  1. If there number are 2a, 5a, and 7a, what will be their LCM?









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    Required LCM = a x 2 x 5 x 7

    Correct Option: A

    Required LCM = a x 2 x 5 x 7 = 70a



  1. What will be the HCF of ( 2 x 3 x 7 x 9 ), ( 2 x 3 x 9 x 11 ) and ( 2 x 3 x 4 x 5 )?









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    ∴ Required HCF = Product of common prime factors having least powers

    Correct Option: C

    Given factors
    2 x 3 x 7 x 9; 2 x 3 x 9 x 11; 2 x 3 x 4 x 5
    ∴ Required HCF = Product of common prime factors having least powers = 2 x 3


  1. Find the LCM of 1/3, 2/9, 5/6 and 4/27.









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    LCM of fractions = (LCM of numerators) / (HCF of denominators)

    Correct Option: C

    We known that,
    LCM of fractions = (LCM of numerators) / (HCF of denominators)

    ∴ Required LCM = (LCM of 1, 2, 5, and 4) / (HCF of 3, 9, 6 and 27)
    ∴ = 20/3



  1. Find the LCM of 2/3, 3/5, 4/7 and 9/13.









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    Required LCM = (LCM of 2, 3, 4, 9) / (HCF of 3, 5, 7, 13)

    Correct Option: A

    Required LCM = (LCM of 2, 3, 4, 9) / (HCF of 3, 5, 7, 13)
    = (4 x 9)/1
    = 36