Question

5. Find the LCM and GCD for 21x²y, 35xy2and verify that
f(x)xg(x) = LCMxGCD.​

Answer 1

Solution :-

LCM : Least common multiple

GCD : greatest common divisor

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21 yx^2 = 3 × 7 × y × x × x

35 xy^2 = 5 × 7 × x × y × y

• LCM = 3 × 5 × 7 × y × y × x × x
• LCM = 105 x^2 y^2

• GCD = 7 × x × y = 7 xy

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we have to verify

that

21 y x^2 × 35x y^2 = LCM × GCD

LHS = 21 yx^2 × 35 xy^2

LHS = 735 x^3 y^3

RHS = LCM × GCD

RHS = 105 x^2 y^2 × 7 x y

RHS = 735 x^3 y^3

LHS = RHS

verified.