Q. 85.0( 1 Vote )

Find the LC

Answer :

Given terms: –


2x2 – 18, 5x2y + 15xy2, x3 + 27y3


Formula used: –


LCM = Least Common Multiple


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


divided completely;


2x2 – 18y2 = 2 × (x2 – 9y2) = 2(x2 – (3y)2) = 2 × (x – 3y) × (x + 3y)


5x2y + 15xy2 = 5 × x × y × (x + 3y)


x3 + 27y3 = (x3 + (3y)3) = (x + 3y)(x2 – 3xy + 9y2)


first find the common factors in all terms


Common factor = (x + 3y)


then multiply the remaining factors of terms in common


factor to get the LCM


= (x + 3y) × [2 × (x – 3y) × 5xy × ( x2 – 3xy + 9y2)]


= 10xy(x + 3y)(x – 3y)( x2 – 3xy + 9y2)]


Conclusion: –


The LCM of given terms [2x2 – 18, 5x2y + 15xy2, x3 + 27y3] is


10xy(x + 3y)(x – 3y)( x2 – 3xy + 9y2)]


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