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 x³ x (3 x + y)²(3 x + 1)(x - 2y)
= 420 x³ (3 x + y)²(3 x + 1)(x - 2y)
lcm worksheet solution2 lcm worksheet solution2