LCM and HCF

LCM and HCF

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Aptitude miscellaneous
  1. The HCF and product of two numbers are 15 and 6300 respectively. The number of possible pairs of the numbers is








  1. View Hint View Answer Discuss in Forum

    Here , HCF = 15
    Let the number be 15p and 15q, where p and q are co – prime.
    With the help of the given formula ,
    HCF × LCM = Product of two numbers
    ∴ 15p × 15q = 6300

    ⇒ pq =
    6300
    		 = 28
    15 × 15

    Correct Option: C

    Here , HCF = 15
    Let the number be 15p and 15q, where p and q are co – prime.
    With the help of the given formula ,
    HCF × LCM = Product of two numbers
    ∴ 15p × 15q = 6300

    ⇒ pq =
    6300
    		 = 28
    15 × 15

    So, two pairs are ( 7 , 4 ) and ( 14 , 2 ) .
    Hence , required answer is 2.

  1. The HCF and LCM of two numbers are 18 and 378 respectively. If one of the number is 54, then the other number is








  1. View Hint View Answer Discuss in Forum

    Given , LCM = 378 , HCF = 18 , First number = 54 , Second number = ?
    As We know that ,

    Second number =
    HCF × LCM
    First number

    Correct Option: A

    Given , LCM = 378 , HCF = 18 , First number = 54 , Second number = ?
    As We know that ,

    Second number =
    HCF × LCM
    First number

    Second number =
    18 × 378
    		 = 126
    54

  1. The product of two numbers is 216. If the HCF is 6, then their LCM is








  1. View Hint View Answer Discuss in Forum

    Let the numbers be 6p and 6q where p and q are prime to each other.
    ∴ 6p × 6q = 216

    ⇒ pq =
    216
    		 = 6
    6 × 6

    Correct Option: D

    Let the numbers be 6p and 6q where p and q are prime to each other.
    ∴ 6p × 6q = 216

    ⇒ pq =
    216
    		 = 6
    6 × 6

    ∴ LCM = 6pq = 6 × 6 = 36

  1. The H.C.F and L.C.M of two numbers are 12 and 336 respectively. If one of the number is 84, the other is








  1. View Hint View Answer Discuss in Forum

    Here , LCM = 336 , HCF = 12 , First number = 84, Second number = ?
    We can find other number with the help of the given formula ,
    First number × second number = HCF × LCM
    ⇒ 84 × second number = 12 × 336

    Correct Option: B

    Here , LCM = 336 , HCF = 12 , First number = 84, Second number = ?
    We can find other number with the help of the given formula ,
    First number × second number = HCF × LCM
    ⇒ 84 × second number = 12 × 336

    ∴ Second number =
    12 × 336
    		 = 48
    84

  1. The H.C.F. and L.C.M. of two numbers are 8 and 48 respectively. If one of the number is 24, then the other number is








  1. View Hint View Answer Discuss in Forum

    Here , LCM = 48 , HCF = 8 , First number = 24 , Second number = ?
    As We know that ,
    First number × second number = HCF × LCM
    ⇒ 24 × second number = 8 × 48

    ∴ Second number =
    8 × 48
    24

    Correct Option: D

    Here , LCM = 48 , HCF = 8 , First number = 24 , Second number = ?
    As We know that ,
    First number × second number = HCF × LCM
    ⇒ 24 × second number = 8 × 48

    ∴ Second number =
    8 × 48
    		 = 16
    24