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1-What-is-the-brief-word-of-LCM-2-If-x-3-and-y-6-then-what-is-the-answer-of-x-2-2xy-y-2-3x-5y-9xy-3-If-a-b-a-b-a-b-then-what-is-the-answer-of-2-3-7-5-9-6-4-Wha

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Question Number 104640 by Anindita last updated on 22/Jul/20
1. What is the brief word of LCM ? 2. If x=3 and y=6 then what is the answer of ((x^2 +2xy+y^2 )/(3x+5y×9xy)) ? 3. If a∗b= ((a×b)/(a÷b)) then what is the answer of 2∗3+7∗5−9∗6 ? 4. What is the brief word of GCD ? What is the GCD of 12,56,80 ? 5. Solve that [(1,6,7),(2,8,9),(3,(−3),(−6)) ]+ [(6,7,(12)),((−6),9,(45)),((−8),6,(−3)) ].
$$\mathrm{1}.\:\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{brief}\:\mathrm{word}\:\mathrm{of}\:\mathrm{LCM}\:? \\ $$$$\mathrm{2}.\:\:\mathrm{If}\:\mathrm{x}=\mathrm{3}\:\mathrm{and}\:\mathrm{y}=\mathrm{6}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\mathrm{answer}\:\mathrm{of}\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}+\mathrm{y}^{\mathrm{2}} }{\mathrm{3x}+\mathrm{5y}×\mathrm{9xy}}\:? \\ $$$$\mathrm{3}.\:\:\mathrm{If}\:\mathrm{a}\ast\mathrm{b}=\:\frac{\mathrm{a}×\mathrm{b}}{\mathrm{a}\boldsymbol{\div}\mathrm{b}}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\mathrm{answer}\:\mathrm{of}\:\mathrm{2}\ast\mathrm{3}+\mathrm{7}\ast\mathrm{5}−\mathrm{9}\ast\mathrm{6}\:? \\ $$$$\mathrm{4}.\:\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{brief}\:\mathrm{word}\:\mathrm{of}\:\mathrm{GCD}\:? \\ $$$$\:\:\:\:\:\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{GCD}\:\mathrm{of}\:\mathrm{12},\mathrm{56},\mathrm{80}\:? \\ $$$$\mathrm{5}.\:\:\mathrm{Solve}\:\mathrm{that} \\ $$$$\:\:\:\:\:\begin{bmatrix}{\mathrm{1}}&{\mathrm{6}}&{\mathrm{7}}\\{\mathrm{2}}&{\mathrm{8}}&{\mathrm{9}}\\{\mathrm{3}}&{−\mathrm{3}}&{−\mathrm{6}}\end{bmatrix}+\begin{bmatrix}{\mathrm{6}}&{\mathrm{7}}&{\mathrm{12}}\\{−\mathrm{6}}&{\mathrm{9}}&{\mathrm{45}}\\{−\mathrm{8}}&{\mathrm{6}}&{−\mathrm{3}}\end{bmatrix}. \\ $$
Answered by Rasheed.Sindhi last updated on 23/Jul/20
1. LCM stands for ′Least Common Multiple ′. 2. ((x^2 +2xy+y^2 )/(3x+5y×9xy))=(((3)^2 +2(3)(6)+(6)^2 )/(3(3)+5(6)×9(3)(6))) =((9+36+36)/(9+30×162))=((81)/(9+4860)) =((81)/(4869))=(9/(541)) 3. 2∗3+7∗5−9∗6=((2×3)/(2÷3))+((7×5)/(7÷5))−((9×6)/(9÷6)) =(2×3)((3/2))+(7×5)((5/7))−(9×6)((6/9)) =(3)(3)+(5)(5)−(6)(6)=9+25−36 =−2 4.GCD stands for ′Greatest Common Divisor′
$$\mathrm{1}.\:\mathrm{LCM}\:\mathrm{stands}\:\mathrm{for}\:'{Least}\:{Common} \\ $$$${Multiple}\:'. \\ $$$$\mathrm{2}.\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}+\mathrm{y}^{\mathrm{2}} }{\mathrm{3x}+\mathrm{5y}×\mathrm{9xy}}=\frac{\left(\mathrm{3}\right)^{\mathrm{2}} +\mathrm{2}\left(\mathrm{3}\right)\left(\mathrm{6}\right)+\left(\mathrm{6}\right)^{\mathrm{2}} }{\mathrm{3}\left(\mathrm{3}\right)+\mathrm{5}\left(\mathrm{6}\right)×\mathrm{9}\left(\mathrm{3}\right)\left(\mathrm{6}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{9}+\mathrm{36}+\mathrm{36}}{\mathrm{9}+\mathrm{30}×\mathrm{162}}=\frac{\mathrm{81}}{\mathrm{9}+\mathrm{4860}} \\ $$$$\:\:\:\:\:\:\:\:\:=\frac{\mathrm{81}}{\mathrm{4869}}=\frac{\mathrm{9}}{\mathrm{541}} \\ $$$$\mathrm{3}.\:\mathrm{2}\ast\mathrm{3}+\mathrm{7}\ast\mathrm{5}−\mathrm{9}\ast\mathrm{6}=\frac{\mathrm{2}×\mathrm{3}}{\mathrm{2}\boldsymbol{\div}\mathrm{3}}+\frac{\mathrm{7}×\mathrm{5}}{\mathrm{7}\boldsymbol{\div}\mathrm{5}}−\frac{\mathrm{9}×\mathrm{6}}{\mathrm{9}\boldsymbol{\div}\mathrm{6}} \\ $$$$=\left(\mathrm{2}×\mathrm{3}\right)\left(\frac{\mathrm{3}}{\mathrm{2}}\right)+\left(\mathrm{7}×\mathrm{5}\right)\left(\frac{\mathrm{5}}{\mathrm{7}}\right)−\left(\mathrm{9}×\mathrm{6}\right)\left(\frac{\mathrm{6}}{\mathrm{9}}\right) \\ $$$$=\left(\mathrm{3}\right)\left(\mathrm{3}\right)+\left(\mathrm{5}\right)\left(\mathrm{5}\right)−\left(\mathrm{6}\right)\left(\mathrm{6}\right)=\mathrm{9}+\mathrm{25}−\mathrm{36} \\ $$$$\:\:\:\:\:\:\:=−\mathrm{2} \\ $$$$\mathrm{4}.\mathrm{GCD}\:{stands}\:{for}\:'{Greatest} \\ $$$${Common}\:{Divisor}' \\ $$

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