Q. 105.0( 2 Votes )

# Find the LCM of the following

10(9x^{2} + 6xy + y^{2}), 12(3x^{2} – 5xy – 2y^{2}), 14(6x^{4} + 2x^{3})

Answer :

__Given terms__: –

10(9x^{2} + 6xy + y^{2}), 12(3x^{2} – 5xy – 2y^{2}), 14(6x^{4} + 2x^{3})

__Formula used__: –

LCM = Least Common Multiple

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

divided completely;

10(9x^{2} + 6xy + y^{2}) = 2 × 5 × ((3x)^{2} + 2 × 3x × y + y^{2})

= 2 × 5 × (3x + y)^{2}

= 2 × 5 × (3x + y) × (3x + y)

12(3x^{2} – 5xy – 2y^{2}) = 2 × 2 × 3 × (3x^{2} – 6xy + xy – 2y^{2})

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

= 2 × 2 × 3 × (x – 2y) × (3x + y)

14(6x^{4} + 2x^{3}) = 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 × x^{3} × (3x + 1))]

2 × 2 × (3x + y)[(5(3x + 4))(3 × (x – 2y))(7 × x^{3} × (3x + 1))]

⇒ then multiply the remaining factors of terms in common

factor to get the LCM

= 2 × 2 × 5 × 3 × 7 × x^{3} × (3x + y)(3x + y)(x – 2y)(3x + 1)

= 420x^{3}(3x + y)^{2}(x – 2y)(3x + 1)

__Conclusion: –__

The LCM of given terms [10(9x^{2} + 6xy + y^{2}), 12(3x^{2} – 5xy – 2y^{2}), 14(6x^{4} + 2x^{3})] is __420x ^{3}(3x + y)^{2}(x – 2y)(3x + 1)__

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