LCM worksheet solution2





In this page LCM worksheet solution2 we are going to see solution of some question with clear explanation.

Definition:

LCM of two or more non zero whole numbers is the smallest whole number which is a multiple of each given number. In other words it must be the smallest whole number which is divisible by each number.

Question 8

Find the LCM of the following

2 x² - 18 y², 5 x² y + 15 x y² , x³ + 27 y³

Solution:

2 x² - 18 y² = 2 (x² - 9 y²)

                = 2 (x² - (3 y)²)

                = 2 (x + 3y) (x - 3y)  

5 x² y + 15 x y² = 5 x y (x + 3 y)

x³ + 27 y³ = x³ + (3 y)³

               = (x + 3 y) (x² + x (3y) + (3y)²)

               = (x + 3 y) (x² + 3 x y + 9 y²)

  L.C.M = 2 (x + 3y) x 5 x y x (x² + 3 x y + 9 y²)

           = 10 x y (x + 3y) (x² + 3 x y + 9 y²)


Question 9

Find the LCM of the following

(x + 4)² ( x - 3)³ , ( x - 1) (x + 4) (x - 3)²

Solution:

  L.C.M = (x + 4)² (x - 3)³ (x - 1)


Question 10

Find the LCM of the following

10 (9 x² + 6 x y + y²) , 12 (3 x² - 5 x y - 2 y²) , 14 (6 x⁴ + 2 x³)

Solution:

10 (9 x² + 6 x y + y²) = 2 x 5 (9 x² + 6 x y + y²)

                              = 2 x 5 (9 x² + 3 x y + 3 x y + y²)

                              = 2 x 5 x [ 3 x (3 x + y) + y (3 x + y) ]

                              = 2 x 5 x (3 x + y) (3 x + y)

                              = 2 x 5 x (3 x + y)²

12 (3 x² - 5 x y - 2 y²) = 2² x 3 (3 x² - 6 x y + x y - 2 y²)

                                = 2² x 3 x [3 x (x - 2y) + y (x - 2y)]

                                = 2² x 3 x (3 x + y) (x - 2y)

          14 (6 x⁴ + 2 x³) = 2 x 7 x 2 x³ (3 x + 1)

                                = 2² x 7 x x³ (3 x + 1)

  L.C.M = 2² x 5 x 7 x 3 x x (3 x + y)²(3 x + 1)(x - 2y)

           = 420 x³ (3 x + y)²(3 x + 1)(x - 2y)

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