LCM Questions and Answers - Form 1 Topical Mathematics

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