Find the LCM of the following

2x² – 18, 5x²y + 15xy², x³ + 27y³

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)]