## LCM and GCD Worksheet

In this page lcm and gcd worksheet we are going to see some practice questions. For each question we have solution with detailed explanation.

(1) Find the LCM of each pair of the following polynomials

(i) x² - 5 x + 6 , x² + 4 x - 12 whose G.C.D is (x - 2) Solution

(ii) x⁴ + 3 x³ + 6 x² + 5 x + 3 , x⁴ + 2 x² + x + 2 whose G.C.D is x² + x + 1  Solution

(iii) 2 x³ + 15 x² + 2 x - 35 , x⁴ + 8 x² + 4 x - 21 whose G.C.D is x + 7  Solution

(iv) 2 x³ - 3 x² - 9 x + 5 , 2 x⁴ - x³ - 10 x² - 11 x + 8

whose G.C.D is 2 x - 1      Solution

(2) Find the other polynomial q (x) of each of the following, given that LCM and GCD and one polynomial p(x) respectively.

(i) (x + 1)² (x + 2)² , (x + 1) (x + 2) , (x + 1)² (x + 2)  Solution

(ii) (4 x + 5)³ (3 x - 7)³ , (4 x + 5) (3 x - 7)² , (4 x + 5)³ (3 x - 7)³  Solution

(iii) (x⁴ - y⁴) (x⁴ + x²y² + y⁴) , x² - y² , x⁴ - y⁴   Solution

(iv) (x³ - 4 x) (5 x + 1) , (5 x² + x) , (5 x³ - 9 x² - 2x) Solution

(v) (x - 1) (x - 2) (x² - 3 x + 3) , (x - 1) , (x³ - 4 x² + 6 x - 3)  Solution

(vi) 2 (x + 1) (x² - 4) , (x + 1), (x + 1) (x - 2)  Solution

Quote on Mathematics

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Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: