LCM and HCF


  1. The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the numbers ?









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    Let the numbers be p and (p + 2).
    ∴ Product of numbers = HCF × LCM
    ⇒ p (p + 2) = 24
    ⇒ p2 + 2p – 24 = 0
    ⇒ p2 + 6p – 4p – 24 = 0
    ⇒ p (p + 6) – 4 (p + 6) = 0
    ⇒ (p – 4) (p + 6) = 0
    ⇒ p = 4 or p = – 6

    Correct Option: D

    Let the numbers be p and (p + 2).
    ∴ Product of numbers = HCF × LCM
    ⇒ p (p + 2) = 24
    ⇒ p2 + 2p – 24 = 0
    ⇒ p2 + 6p – 4p – 24 = 0
    ⇒ p (p + 6) – 4 (p + 6) = 0
    ⇒ (p – 4) (p + 6) = 0
    ⇒ p = 4 or p = – 6
    Numbers = p = 4 and p + 2 = 4 + 2 = 6.
    ∴ Numbers are 4 and 6.


  1. The H.C.F. and L.C.M. of two numbers are 21 and 84 respectively. If the ratio the two numbers is 1 : 4, then the larger of the two numbers is









  1. View Hint View Answer Discuss in Forum

    HCF of numbers = 21
    ∴ Numbers = 21p and 21q Where p and q are prime to each other.
    Ratio of numbers = 1 : 4

    Correct Option: D

    HCF of numbers = 21
    ∴ Numbers = 21p and 21q Where p and q are prime to each other.
    Ratio of numbers = 1 : 4
    ∴ Larger number = 21 × 4 = 84



  1. If p : q be the ratio of two whole numbers and r be their HCF, then the LCM of those two numbers is









  1. View Hint View Answer Discuss in Forum

    We can find the LCM with the help of given formula ,
    Product of two numbers = HCF × LCM
    ⇒ Numbers = rp and rq
    ∴ rp × rq = r × LCM

    Correct Option: D

    We can find the LCM with the help of given formula ,
    Product of two numbers = HCF × LCM
    ⇒ Numbers = rp and rq
    ∴ rp × rq = r × LCM
    ⇒ LCM = pqr
    Hence , the LCM of two numbers is pqr.


  1. Three numbers are in the ratio 1 : 2 : 3 and their HCF is 12. The numbers are









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    Let the numbers are p , 2p and 3p .
    Their H.C.F. = p = 12

    Correct Option: A

    Let the numbers are p , 2p and 3p .
    Their H.C.F. = p = 12
    ∴ Numbers = p = 12, 2p = 2 × 12 = 24 and 3p = 3 × 12 = 36
    Hence , Three numbers are 12 , 24 and 36 .



  1. The ratio of two numbers is 3 : 4 and their HCF is 5. Their LCM is :









  1. View Hint View Answer Discuss in Forum

    If the numbers be 3p and 4p, then
    HCF = p = 5
    ∴ Numbers = 3p = 3 × 5 = 15 and 4p = 4 × 5 = 20

    Correct Option: B

    If the numbers be 3p and 4p, then
    HCF = p = 5
    ∴ Numbers = 3p = 3 × 5 = 15 and 4p = 4 × 5 = 20
    ∴ LCM = 60