LCM and HCF


  1. If a number is exactly divisible by 11 and 13, which of the following types the number must be?











  1. View Hint View Answer Discuss in Forum

    LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13).

    Correct Option: C

    LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13).


  1. The LCM of two numbers is 48. The numbers are in the ratio of 2 : 3. Find the sum of the numbers.









  1. View Hint View Answer Discuss in Forum

    Let numbers are 2N and 3N.
    According to the question, 6N = 48
    ⇒ N = 8 ( ∵ LCM = 6N )
    ∴ Required sum = ( 2N + 3N ) = 5N

    Correct Option: C

    Let numbers are 2N and 3N.
    According to the question, 6N = 48
    ⇒ N = 8 ( ∵ LCM = 6N )
    ∴ Required sum = ( 2N + 3N ) = 5N
    = 5 x 8 = 40



  1. The Product of two whole numbers is 1500 and their HCF is 10, Find the LCM.











  1. View Hint View Answer Discuss in Forum

    According to the formula,
    Product of two numbers = HCF x LCM

    Correct Option: B

    Given that, product of two numbers =1500
    HCF = 10
    According to the formula,
    Product of two numbers = HCF x LCM
    ⇒ 1500 = 10 x LCM
    ∴ LCM = 1500/10 =150


  1. The least number which should be added to 2497, so that the sum is exactly divisible by 5, 6, 4 and 3, is











  1. View Hint View Answer Discuss in Forum

    LCM of 5, 6, 4 and 3 = 60
    On dividing 2497 by 60, the remainder is 37.
    ∴ Number to be added = 60 - 37

    Correct Option: C

    LCM of 5, 6, 4 and 3 = 60
    On dividing 2497 by 60, the remainder is 37.
    ∴ Number to be added = 60 - 37 = 23



  1. The least number which when divided by 12,16 and 18 leaves 5 as remainder in each case. Find the number.











  1. View Hint View Answer Discuss in Forum

    Given, a = 12, b =16 , c =18, k = 5
    According to the formula,
    Required number =(LCM of a, b and c) + k
    = (LCM Of 12, 16, 18) + 5

    LCM of 12, 16, 18 is
    ∴ LCM = 2 x 2 x 3 x 4 x 3 = 144

    ∴ Required number =144 + 5 = 149

    Correct Option: C

    Given, a = 12, b =16 , c =18, k = 5
    According to the formula,
    Required number =(LCM of a, b and c) + k
    = (LCM Of 12, 16, 18) + 5

    LCM of 12, 16, 18 is
    ∴ LCM = 2 x 2 x 3 x 4 x 3 = 144

    ∴ Required number =144 + 5 = 149