LCM and HCF


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









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    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









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    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









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    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









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    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