LCM Questions and Answers - Form 1 Topical Mathematics

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Questions

  1. A piece of land is to be divided into 20 acres or 24 acres or 26 acres or 28 acres for farming and leave 7 acres for grazing. Determine the smallest size of such land.
  2. When a certain number x is divided by 30, 45 or 54, there is always a remainder of 21. Find the least value of the number x
  3. A number m is such that when it is divided by 30, 36, and 45, the remainder is always 7. Find the smallest possible value of m.
  4. Find the L.C.M of x2 + x , x2 – 1 and x2 – x

Answers

  1.  
     2 20 24 26 28
     2  10 12  13  14
     2  5  6  13  7
     3  5  3  13  7
     5  5  1  13  7
     7  1  1  13  7
     13  1  1  13  1
     1  1  1  1  1

    Size of the land = ((23 x 3 x 5 x 7 x 13) + 7) acres
    = 10920 + 7 = 10,927 acres
  2.  2 30 45 54
    3 15 45 27
    3 5 15 9
    3 5 5 1
    5 5 5 1
    1 1 1 1
    Least value of x = (2 x 33 x 5) + 21
    =270 + 21 = 291
  3. 2 30 36 45
    2 15 18 45
    3 15 9 45
    3 5 3 15
    5 5 1 5
      1 1 1
    Smallest value of m = (22 x 33 x 5) + 7 = 187
  4. x2 + x = x (x + 1)
    x2 -1 = (x + 1) (x – 1)
    x2 – x = x(x – 1)
    x(x+1) (x – 1)
    x3- x

 


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