LCM and HCF


  1. The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M.?









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    Here , HCF of two numbers is 8.
    This means 8 is a factor common to both the numbers. LCM is common multiple for the two numbers, it is divisible by the two numbers.

    Correct Option: D

    Here , HCF of two numbers is 8.
    This means 8 is a factor common to both the numbers. LCM is common multiple for the two numbers, it is divisible by the two numbers. So, the required answer = 60


  1. The HCF and LCM of two numbers are 13 and 455 respectively. If one of the number lies between 75 and 125, then, that number is :









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    Given that , HCF = 13 , LCM = 455
    Let the numbers be 13p and 13q , Where p and q are co-prime.
    ∴ LCM = 13pq
    ∴ 13pq = 455

    ∴ pq =
    455
    13

    Correct Option: B

    Given that , HCF = 13 , LCM = 455
    Let the numbers be 13p and 13q , Where p and q are co-prime.
    ∴ LCM = 13pq
    ∴ 13pq = 455

    ∴ pq =
    455
    = 35 = 5 × 7
    13

    ∴ Numbers are 13 × 5 = 65 and 13 × 7 = 91



  1. The product of two numbers is 2028 and their HCF is 13. The number of such pairs is









  1. View Hint View Answer Discuss in Forum

    Here, HCF = 13
    Let the numbers be 13p and 13q ,where p and q are Prime to each other.
    Now, 13p × 13q = 2028

    ⇒ pq =
    2028
    = 12
    13 × 13

    Correct Option: B

    Here, HCF = 13
    Let the numbers be 13p and 13q ,where p and q are Prime to each other.
    Now, 13p × 13q = 2028

    ⇒ pq =
    2028
    = 12
    13 × 13

    The possible pairs are :- ( 1 , 12 ) , ( 3 , 4 ) , ( 2 , 6 )
    But the 2 and 6 are not co-prime.
    ∴ The required no. of pairs = 2


  1. LCM of two numbers is 2079 and their HCF is 27. If one of the number is 189, the other number is









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    Here , LCM = 2079 , HCF = 27 , First number = 189, Second number = ?
    We can find other number with the help of the given formula ,

    Second number =
    H.C.F. × L.C.M.
    First Number

    Correct Option: A

    Here , LCM = 2079 , HCF = 27 , First number = 189, Second number = ?
    We can find other number with the help of the given formula ,

    Second number =
    H.C.F. × L.C.M.
    First Number

    Second number =
    27 × 2079
    = 297
    189



  1. The product of two numbers is 2160 and their HCF is 12. Number of such possible pairs is









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    Given that , HCF = 12
    Let Numbers are 12p and 12q , where p and q are prime to each other.
    ∴ 12p × 12q = 2160

    ⇒ pq =
    2160
    = 15
    12 × 12

    Correct Option: B

    Given that , HCF = 12
    Let Numbers are 12p and 12q , where p and q are prime to each other.
    ∴ 12p × 12q = 2160

    ⇒ pq =
    2160
    = 15
    12 × 12

    Possible Factors of 15 = 3 × 5, 1 × 15
    So , Possible pairs = ( 36 , 60 ) and ( 12 , 180 ) .
    Hence , Number of such possible pairs is 2.