LCM and HCF


  1. The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35, is









  1. View Hint View Answer Discuss in Forum

    We find LCM of 20, 28, 32 and 35

    ∴ LCM = 2 × 2 × 5 × 7 × 8 = 1120
    ∴ Required number = 5834 – LCM of 20, 28, 32 and 35

    Correct Option: B

    We find LCM of 20, 28, 32 and 35

    ∴ LCM = 2 × 2 × 5 × 7 × 8 = 1120
    ∴ Required number = 5834 – LCM of 20, 28, 32 and 35
    ∴ Required number = 5834 – 1120 = 4714


  1. The smallest perfect square divisible by each of 6, 12 and 18 is









  1. View Hint View Answer Discuss in Forum

    The LCM of 6, 12 and 18 = 36 = 62

    Correct Option: D

    The LCM of 6, 12 and 18 = 36 = 62 = 36
    Hence , required answer is 36.



  1. The LCM fo two prime numbers p and q, (p > q) is 161. The value of (3q – p) :









  1. View Hint View Answer Discuss in Forum

    LCM of p and q = 161
    ∴ pq = 23 × 7
    ∴ p = 23; q = 7
    ∴ 3q – p = 3 × 7 – 23

    Correct Option: A

    LCM of p and q = 161
    ∴ pq = 23 × 7
    ∴ p = 23; q = 7
    ∴ 3q – p = 3 × 7 – 23
    The value of (3q – p) = 21 – 23 = – 2


  1. The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to the fourth number. What is the sum of four numbers?









  1. View Hint View Answer Discuss in Forum

    We find LCM of 60 ,

    ∴ 60 = 2 × 2 × 3 × 5
    i.e., Numbers = 2, 3, 4 and 5

    Correct Option: B

    We find LCM of 60 ,

    ∴ 60 = 2 × 2 × 3 × 5
    i.e., Numbers = 2, 3, 4 and 5
    ∴ Required sum = 2 + 3 + 4 + 5 = 14



  1. Three bells ring at intervals of 36 seconds, 40 seconds and 48 seconds respectively. They start ringing together at a particular time. They will ring together after every









  1. View Hint View Answer Discuss in Forum

    Required answer = LCM of 36, 40 and 48 seconds

    ∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720

    Correct Option: B

    Required answer = LCM of 36, 40 and 48 seconds
    = 720 seconds

    Required answer =
    720
    minutes = 12 minutes
    60


    ∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720