LCM and HCF


  1. The greatest possible length which can be used to measure exactly the lengths 7m, 3m 85cm, 12m 95 cm, is ?









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    Required length = H.C.F of 700, 385, 1295 cm

    Correct Option: C

    Required length = H.C.F of 700, 385, 1295 cm
    = 35 cm.


  1. The sum of two number is 216 and their H.C.F is 27. The numbers are ?









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    Let the number be 27a and 27b
    Then, 27a + 27b = 216
    or a + b = 216/27 = 8
    ∴ Values of co-primes with sum 8 are (1, 7) and (3, 5)
    So, the number are (27 x 1 , 27 x 7) i.e. (27, 189)

    Correct Option: C

    Let the number be 27a and 27b
    Then, 27a + 27b = 216
    or a + b = 216/27 = 8
    ∴ Values of co-primes with sum 8 are (1, 7) and (3, 5)
    So, the number are (27 x 1 , 27 x 7) i.e. (27, 189)



  1. The product of two-digit numbers is 2160 and their G.C.M is 12. The numbers are ?









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    Let the number be 12a and 12b
    Then 12a x 12b = 2160
    or ab = 15
    ∴ Values of co-primes a and b are (1, 15), (3, 5)
    So, the two digit number are 12 x 3 and 12 x 5 i.e. 36 and 60 .

    Correct Option: B

    Let the number be 12a and 12b
    Then 12a x 12b = 2160
    or ab = 15
    ∴ Values of co-primes a and b are (1, 15), (3, 5)
    So, the two digit number are 12 x 3 and 12 x 5 i.e. 36 and 60 .


  1. The H.C.F of two number is 16 and their L.CM is 160. If one of the numbers is 32, then the other number is ?









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    Product of two numbers = LCM of two numbers x HCF of two numbers.
    ⇒ N x 32 = 160 x 16
    ∴ N = 80

    Correct Option: B

    Product of two numbers = LCM of two numbers x HCF of two numbers.
    ⇒ N x 32 = 160 x 16
    ∴ N = 80



  1. The product of two numbers is 1600 and their H.C.F is 5. The L.C.M. of the numbers is ?









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    Product of two numbers = LCM of two numbers x HCF of two numbers.

    Correct Option: A

    Product of two numbers = LCM of two numbers x HCF of two numbers.
    ⇒ 1600 = LCM x 5
    ∴ LCM = 320