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L.C.M Questions

1.  a) Find the greatest common divisor of the term. (1 mark)

 

144x3y2 and 81xy4

 b) Hence factorise completely this expression 144x3y2-81xy4  (2 marks)

2.  The GCD of two numbers is 7and their LCM is 140. if one of the numbers is 20, find the other number (2mks)

3.  The LCM of three numbers is 7920 and their GCD is 12. Two of the numbers are 48 and 264. Using factor notation find the third number if one of its factors is 9. (3mks)

4.  Find the least number of sweets that can be packed into polythene bags which contain either 9 or 15 or 20 or 24 sweets with none left over.  (3mks)

5.  A number n is such that when it is divided by 27, 30, or 45, the remainder is always 3. Find the smallest value of n.  (2 mks)

6.  A piece of land is to be divided into 20 acres or 24 acres or 28 acres for farming and

leave 7 acres for grazing. Determine the smallest size of such land.  

 

7. 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

 

8.  A number m is such that when it is divided by 30, 36, and 45, the remainder is always 7. Find the

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smallest possible value of m.

 

9.  Find the L.C.M of x2 + x , x2 – 1 and x2 – x  

 

L.C.M Answers

 

1.

  1. G.C.D of 81xy4 and

144x3y2 is 9xy2

144x3y2 – 81xy4

9xy2(16x2 – 9y2)

9xy2(4x – 3y) (4x + 3y)

 

M1

 

 

M1

 

A1

 
  

3

 

2.

Let the other number be x

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M1

 

 

 

 

A1

 
  

02

 

3.

LCM = 7920 = 24x32x5x11

GCD = 12 = 22×3

48 = 24×3

264 = 23x3x11

X = 22x32x5

X = 180

M1

 

M1

 

 

A1

Factor notation GCD and LCM

Factor notation 2numbers

 

 

C.A.O

  

03

 

4.

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M1

 

 

M1

 

 

 

 

A1

 

 

Correct factors

 

 

Accept other alternative correct method for getting the L.C.M

  

03

 

5.

L.C.M =

2 27 30 45

3 27 15 45

3 9 5 15

3 3 5 5

5 1 5 5

1 1 1

2x33x5 = 270

= 270 + 3 = 273.

 

 

M1

 

 

 

 

 

A1

 

 

LCM

  

02

 

 

6.  2 20, 24, 26, 28

  2 10 12 13 14

  2 5 6 13 7

  3 2 3 13 7

 5 5 1 13 7

7 1 1 13 7

 13 1 1 13 1

1 1 1 1

  Size of the land = (23 x 3 x 5 x 7 x 13) + 7) aces

= 10920 + 7 = 10,927 aces

7.  

2

30

45

54

3

3

3

5

15

5

5

5

1

45

15

5

5

1

27

9

3

1

1

Least volume of x = 2 X 33 x 5 + 21

= 270 + 21 = 291

 

8.  L.C.M. of 30, 36 and 45

 

2 30 36 45

2 15 18 45

3 15 9 45

3 5 3 15

5 5 1 5

1 1

 

 L.C.M. = 22 x 32 x 5 = 180

 The number m = 180 + 7 = 187

 

9.  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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