# Find the LCM of the following10(9x2 + 6xy + y2), 12(3x2 – 5xy – 2y2), 14(6x4 + 2x3)

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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