LCM and HCF

LCM and HCF

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  1. The H.C.F. and L.C.M. of two 2-digit numbers are 16 and 480 respectively. The numbers are :








  1. View Hint View Answer Discuss in Forum

    Given that ,
    L.C.M. of the two 2-digit numbers = 480
    H.C.F. of the two 2-digit numbers = 16
    Hence, the numbers can be expressed as 16p and 16q, where p and q are prime to each other.
    As we know that ,
    First number × second number = H.C.F. × L.C.M.
    ⇒ 16p × 16q = 16 × 480

    ⇒ pq =
    16 × 480
    		= 30
    16 × 16

    Correct Option: D

    Given that ,
    L.C.M. of the two 2-digit numbers = 480
    H.C.F. of the two 2-digit numbers = 16
    Hence, the numbers can be expressed as 16p and 16q, where p and q are prime to each other.
    As we know that ,
    First number × second number = H.C.F. × L.C.M.
    ⇒ 16p × 16q = 16 × 480

    ⇒ pq =
    16 × 480
    		= 30
    16 × 16

    The possible pairs of p and q, satisfying the condition pq = 30 are :- (3, 10), (5, 6), (1, 30), (2, 15)
    Since the numbers are of 2-digits each.
    Hence, admissible pair is (5, 6)
    i.e. p = 5 and q = 6
    ∴ Numbers are : 16p = 16 × 5 = 80 and 16q = 16 × 6 = 96

  1. The HCF of two numbers 12906 and 14818 is 478. Their LCM is








  1. View Hint View Answer Discuss in Forum

    Here , LCM = ? , HCF = 478 , First number = 12906, Second number = 14818
    With the help of the given formula ,
    Product of two numbers = HCF × LCM
    ⇒ 12906 × 14818 = LCM × 478

    Correct Option: A

    Here , LCM = ? , HCF = 478 , First number = 12906, Second number = 14818
    With the help of the given formula ,
    Product of two numbers = HCF × LCM
    ⇒ 12906 × 14818 = LCM × 478

    ⇒ LCM =
    12906 × 14818
    		= 400086
    478

  1. The LCM of two numbers is 1920 and their HCF is 16. If one of the number is 128, find the other number.








  1. View Hint View Answer Discuss in Forum

    Given ,LCM = 1920 , HCF = 16 , First number = 128 , Second number = ?
    As We know that ,
    First number × second number = LCM × HCF

    ∴ Second number =
    LCM × HCF
    First number

    Correct Option: B

    Given ,LCM = 1920 , HCF = 16 , First number = 128 , Second number = ?
    As We know that ,
    First number × second number = LCM × HCF

    ∴ Second number =
    LCM × HCF
    First number

    ∴ Second number =
    1920 × 16
    		= 45
    240

  1. The HCF of two numbers is 16 and their LCM is 160. If one of the number is 32, then the other number is








  1. View Hint View Answer Discuss in Forum

    Given ,LCM = 160 , HCF = 16 , First number = 32 , Second number = ?
    We know that,
    First number × Second number = LCM × HCF

    Correct Option: B

    Given ,LCM = 160 , HCF = 16 , First number = 32 , Second number = ?
    We know that,
    First number × Second number = LCM × HCF

    ⇒ Second number =
    16 × 160
    		 = 80
    32

  1. LCM of two numbers is 225 and their HCF is 5. If one number is 25, the other number will be:








  1. View Hint View Answer Discuss in Forum

    Given , LCM = 225 , HCF = 5 , First Number = 25 , Second Number = ?
    We can find the Second Number with the help of given formula ,
    LCM × HCF = 1st Number× 2nd Number
    ⇒ 225 × 5 = 25 × 2nd Number

    Correct Option: C

    Given , LCM = 225 , HCF = 5 , First Number = 25 , Second Number = ?
    We can find the Second Number with the help of given formula ,
    LCM × HCF = 1st Number× 2nd Number
    ⇒ 225 × 5 = 25 × 2nd Number

    2nd Number =
    225 × 5
    		= 45
    25