LCM and HCF

LCM and HCF

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Aptitude miscellaneous
  1. The product of two numbers is 1280 and their H.C.F. is 8. The L.C.M. of the number will be :








  1. View Hint View Answer Discuss in Forum

    Given that , Product of two numbers = 1280
    HCF = 8 , LCM = ?
    We can find LCM with the help of the given formula ,
    HCF × LCM = Product of two numbers
    ⇒ 8 × LCM = 1280

    Correct Option: A

    Given that , Product of two numbers = 1280
    HCF = 8 , LCM = ?
    We can find LCM with the help of the given formula ,
    HCF × LCM = Product of two numbers
    ⇒ 8 × LCM = 1280

    ⇒ LCM =
    1280
    		 = 160
    8

  1. The LCM of two numbers is 30 and their HCF is 5. One of the number is 10. The other is








  1. View Hint View Answer Discuss in Forum

    Here , LCM = 30 , HCF = 5 , First number = 10, Second number = 14818
    As we know that ,
    First number × second number = LCM × HCF
    Let the second number be p.
    ∴ 10p = 30 × 5

    ⇒ p =
    30 × 5
    10

    Correct Option: C

    Here , LCM = 30 , HCF = 5 , First number = 10, Second number = 14818
    As we know that ,
    First number × second number = LCM × HCF
    Let the second number be p.
    ∴ 10p = 30 × 5

    ⇒ p =
    30 × 5
    		 = 15
    10

  1. The HCF and LCM of two numbers are 12 and 924 respectively. Then the number of such pairs is








  1. View Hint View Answer Discuss in Forum

    Here , HCF and LCM of two numbers are 12 and 924 .
    Let the numbers be 12p and 12q where p and q are prime to each other.
    ∴ LCM = 12pq
    ∴ 12pq = 924
    ⇒ pq = 77

    Correct Option: C

    Here , HCF and LCM of two numbers are 12 and 924 .
    Let the numbers be 12p and 12q where p and q are prime to each other.
    ∴ LCM = 12pq
    ∴ 12pq = 924
    ⇒ pq = 77
    ∴ Possible pairs = ( 1 , 77 ) and ( 7 ,11 )
    Hence , required answer is 2.

  1. The HCF of two numbers is 15 and their LCM is 300. If one of the number is 60, the other is :








  1. View Hint View Answer Discuss in Forum

    Given that , LCM = 300 , HCF = 15 , First number = 60 , Second number = ?
    With the help of the given formula ,
    First number × Second number = HCF × LCM

    ∴ Second number =
    15 × 300
    60

    Correct Option: B

    Given that , LCM = 300 , HCF = 15 , First number = 60 , Second number = ?
    With the help of the given formula ,
    First number × Second number = HCF × LCM

    ∴ Second number =
    15 × 300
    		 = 75
    60

  1. The product of two numbers is 4107. If the H.C.F. of the numbers is 37, the greater number is








  1. View Hint View Answer Discuss in Forum

    We can find required answer with the help of given formula ,

    LCM =
    Product of two numbers
    HCF

    LCM =
    4107
    		= 111
    37

    Correct Option: B

    We can find required answer with the help of given formula ,

    LCM =
    Product of two numbers
    HCF

    LCM =
    4107
    		= 111
    37

    Obviously, numbers are 111 and 37 which satisfy the given condition.
    Hence, the greater number = 111