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Quiz: Number System and HCF & LCM

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Number of Questions: 43

Question: 21 -

Find the smallest number of 4 digits which is exactly divisible by 12, 15, 21 and 30. 

Options:

  1. 1420

  2. 1260

  3. 1580

  4. 1056

    5. Answer:

    1260
    Solution:

    Least 4 digit number = 1000
    LCM of (12, 15, 21, 30) = 420
    On dividing 420 by 1000, leaves remainder = 160
    So answer = 1000 + (420 – 160)

Question: 22 -

Find the least number which when divided by15, 21, 24 and 32 leaves the same remainder 2 in each case. 

Options:

  1. 3456

  2. 3266

  3. 3362

  4. 3360

    5. Answer:

    3362
    Solution:

    It will be the LCM of these numbers + 2
    So 3360 + 2

Question: 23 -

The sum of three consecutive even numbers is 42. Find the middle number of the three?

Options:

  1. 18

  2. 16

  3. 14

  4. 24

    5. Answer:

    14
    Solution:

    Three consecutive even numbers (2P - 2), 2P, (2P + 2).
    (2P - 2) + 2P + (2P + 2) = 42
    6P = 42 => P = 7.
    The middle number is: 2P = 14.

Question: 24 -

What least number must be subtracted from 13601, so that the remainder is divisible by 87 ?

Options:

  1. 23

  2. 37

  3. 29

  4. 31

    5. Answer:

    29
    Solution:

    87)13601(156
           87 
           -----
           490
           435
            -----
            551
            522
             -----
             29
             -----
    Required number is 29.

Question: 25 -

Two containers contain 50 and 125 litres of water respectively. Find the maximum capacity of a container which can measure the water in each container an exact number of times(in litres)

Options:

  1. 11

  2. 25

  3. 15

  4. 12

    5. Answer:

    25
    Solution:

    HCF of 50 and 125 = 25