LCM and HCF

LCM and HCF

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








  1. View Hint View Answer Discuss in Forum

    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 :








  1. View Hint View Answer Discuss in Forum

    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








  1. View Hint View Answer Discuss in Forum

    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








  1. View Hint View Answer Discuss in Forum

    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.