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HCF And LCM of Numbers Test-2

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HCF And LCM of Numbers Test-2
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  • Question 1
    1 / -0.25

    A rectangular courtyard 140cm long 525cm wide is to be paved exactly with square  tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?

    Solution

     

    30 cm = 4 ×5 ×7
    525 cm = 5 ×5 ×3 ×7
    Hence common factors are 5 and 7
    Hence LCM = 5 ×7 = 35

  • Question 2
    1 / -0.25

    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)

    Solution

    HCF of 50 and 125 = 25

  • Question 3
    1 / -0.25

    Two baskets contain 183 and 242 Apples respectively, which are distributed in equal number among children. Find the largest number of apples that can be given, so that 3 apples are left over from the first basket and 2 from the second.

    Solution

    183-3 = 180
    142-2 = 240
    HCF of 240, 180 = 60

  • Question 4
    1 / -0.25

    A person has 3 bars whose length are 12,16,24m respectively. He want to cuts the longest possible pieces, all of the same length from each of the 3 bars, what is the length of the each piece, if he is cut without any wastage

    Solution

    HCF of 12, 16, 24 = 4m

  • Question 5
    1 / -0.25

    Four bells commence tolling together and toll at the intervals of 3,9,12,15 seconds resp. In 60 minutes how many times they will toll together.

    Solution

    LCM of 3, 9, 12, 15 = 180s = 3m
    In 60m = 60/3 = 20 ⇒20+1 = 21

  • Question 6
    1 / -0.25

    In a seminar the number of participants in Technology, Economics and Science are 150, 90 and 180 respectively. Find the minimum number of rooms required, where in each room the same number of participants are to be seated and all of them being in the same subject.

    Solution

    HCF of 150, 90 and 180 = 30
    No of participants can be seated in each room = 30  

    There are total 420 participants.

    As the HCF is 30 i.e. mininum number of participants in each room.

    so total rooms required will be 420/30 = 14

  • Question 7
    1 / -0.25

    Naren, Suraj and Praveen start running around a circular stadium and complete one round in 12s, 9s and 15s respectively. In how much time will they meet again at the starting point ?

    Solution

    LCM of 12, 9, 15 =180s = 3m

  • Question 8
    1 / -0.25

    Three boxes of lengths 60m,30m and 45m are to be cut into pieces of equal length. What is the greatest possible length of each pieces ?

    Solution

    HCF of 60, 30 and 45m = 15m

  • Question 9
    1 / -0.25

    In a college, all the students can stand in a row, so that each row has 9, 7 and 12 students. Find the least no of students in the school ?

    Solution

    LCM of 9, 7 and 12 = 252

  • Question 10
    1 / -0.25

     

    The HCF of 3 different no is 17, Which of the following cannot be their LCM ?

    Solution

     

    To check whether the given number is it 's LCM or not just divide the LCM by HCF .

    1) 540 ÷17 = 31.76

    2) 289 ÷17 = 17

    3) 340 ÷17 = 20

    4) 425 ÷17 = 25 .

    540 is not divisible by 17.

    Hence : 540 is not the LCM .

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