Q. 105.0( 2 Votes )

Find the LCM of the following

10(9x2 + 6xy + y2), 12(3x2 – 5xy – 2y2), 14(6x4 + 2x3)

Answer :

Given terms: –


10(9x2 + 6xy + y2), 12(3x2 – 5xy – 2y2), 14(6x4 + 2x3)


Formula used: –


LCM = Least Common Multiple


Means it is the lowest term by which every element must be


divided completely;


10(9x2 + 6xy + y2) = 2 × 5 × ((3x)2 + 2 × 3x × y + y2)


= 2 × 5 × (3x + y)2


= 2 × 5 × (3x + y) × (3x + y)


12(3x2 – 5xy – 2y2) = 2 × 2 × 3 × (3x2 – 6xy + xy – 2y2)


= 2 × 2 × 3 × (3x(x – 2y) + y(x – 2y))


= 2 × 2 × 3 × (x – 2y) × (3x + y)


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


first find the common factors in all terms


Common factor = 2


Common factors in any 2 terms


2 × [(5(3x + 4)2)(2 × 3 × (x – 2y)(3x + y))(7 × 2 × x3 × (3x + 1))]


2 × 2 × (3x + y)[(5(3x + 4))(3 × (x – 2y))(7 × x3 × (3x + 1))]


then multiply the remaining factors of terms in common


factor to get the LCM


= 2 × 2 × 5 × 3 × 7 × x3 × (3x + y)(3x + y)(x – 2y)(3x + 1)


= 420x3(3x + y)2(x – 2y)(3x + 1)


Conclusion: –


The LCM of given terms [10(9x2 + 6xy + y2), 12(3x2 – 5xy – 2y2), 14(6x4 + 2x3)] is 420x3(3x + y)2(x – 2y)(3x + 1)


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