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Question Number 177930 by Spillover last updated on 11/Oct/22

Find the LCM 14a^2 b^3 c^4 ,20ab^4 c^4 and 35a^5 b^3 c

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{LCM}\: \\ $$$$\mathrm{14a}^{\mathrm{2}} \mathrm{b}^{\mathrm{3}} \mathrm{c}^{\mathrm{4}} ,\mathrm{20ab}^{\mathrm{4}} \mathrm{c}^{\mathrm{4}} \:\mathrm{and} \\ $$$$\:\mathrm{35a}^{\mathrm{5}} \mathrm{b}^{\mathrm{3}} \mathrm{c} \\ $$

Answered by Ar Brandon last updated on 11/Oct/22

determinant (((abc),(14a^2 b^3 c^4 ),(20ab^4 c^4 ),(35a^5 b^3 c)),(b^2 ,(14ab^2 c^3 ),(20b^3 c^3 ),(35a^4 b^2 )),(b,(14ac^3 ),(20bc^3 ),(35a^4 )),(c^3 ,(14ac^3 ),(20c^3 ),(35a^4 )),(a,(14a),(20),(35a^4 )),(a^3 ,(14),(20),(35a^3 )),(7,(14),(20),(35)),(5,2,(20),5),(2,2,4,1),(2,1,2,1),(,1,1,1)) L.C.M=abc×b^2 ×b×c^3 ×a×a^3 ×7×5×2×2 =140a^5 b^4 c^4

$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}{{abc}}&\hline{\mathrm{14}{a}^{\mathrm{2}} {b}^{\mathrm{3}} {c}^{\mathrm{4}} }&\hline{\mathrm{20}{ab}^{\mathrm{4}} {c}^{\mathrm{4}} }&\hline{\mathrm{35}{a}^{\mathrm{5}} {b}^{\mathrm{3}} {c}}\\{{b}^{\mathrm{2}} }&\hline{\mathrm{14}{ab}^{\mathrm{2}} {c}^{\mathrm{3}} }&\hline{\mathrm{20}{b}^{\mathrm{3}} {c}^{\mathrm{3}} }&\hline{\mathrm{35}{a}^{\mathrm{4}} {b}^{\mathrm{2}} }\\{{b}}&\hline{\mathrm{14}{ac}^{\mathrm{3}} }&\hline{\mathrm{20}{bc}^{\mathrm{3}} }&\hline{\mathrm{35}{a}^{\mathrm{4}} }\\{{c}^{\mathrm{3}} }&\hline{\mathrm{14}{ac}^{\mathrm{3}} }&\hline{\mathrm{20}{c}^{\mathrm{3}} }&\hline{\mathrm{35}{a}^{\mathrm{4}} }\\{{a}}&\hline{\mathrm{14}{a}}&\hline{\mathrm{20}}&\hline{\mathrm{35}{a}^{\mathrm{4}} }\\{{a}^{\mathrm{3}} }&\hline{\mathrm{14}}&\hline{\mathrm{20}}&\hline{\mathrm{35}{a}^{\mathrm{3}} }\\{\mathrm{7}}&\hline{\mathrm{14}}&\hline{\mathrm{20}}&\hline{\mathrm{35}}\\{\mathrm{5}}&\hline{\mathrm{2}}&\hline{\mathrm{20}}&\hline{\mathrm{5}}\\{\mathrm{2}}&\hline{\mathrm{2}}&\hline{\mathrm{4}}&\hline{\mathrm{1}}\\{\mathrm{2}}&\hline{\mathrm{1}}&\hline{\mathrm{2}}&\hline{\mathrm{1}}\\{}&\hline{\mathrm{1}}&\hline{\mathrm{1}}&\hline{\mathrm{1}}\\\hline\end{array} \\ $$$${L}.{C}.{M}={abc}×{b}^{\mathrm{2}} ×{b}×{c}^{\mathrm{3}} ×{a}×{a}^{\mathrm{3}} ×\mathrm{7}×\mathrm{5}×\mathrm{2}×\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{140}{a}^{\mathrm{5}} {b}^{\mathrm{4}} {c}^{\mathrm{4}} \\ $$

Commented by Spillover last updated on 11/Oct/22

Thank you very much.you have done the question in a short time

$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}.\mathrm{you}\:\mathrm{have} \\ $$$$\mathrm{done}\:\mathrm{the}\:\mathrm{question}\:\mathrm{in}\:\mathrm{a}\:\mathrm{short}\:\mathrm{time} \\ $$

Answered by Spillover last updated on 11/Oct/22

14,20 35 LCM=140 a^2 a a^5 LCM=a^5 c^4 ,c^3 c LCM=c^4 LCM=140×a^5 ×a^4

$$\mathrm{14},\mathrm{20}\:\mathrm{35}\:\:\:\mathrm{LCM}=\mathrm{140} \\ $$$$\mathrm{a}^{\mathrm{2}} \:\:\mathrm{a}\:\:\mathrm{a}^{\mathrm{5}} \:\:\:\:\mathrm{LCM}=\mathrm{a}^{\mathrm{5}} \\ $$$$\mathrm{c}^{\mathrm{4}} ,\mathrm{c}^{\mathrm{3}} \:\mathrm{c}\:\:\:\mathrm{LCM}=\mathrm{c}^{\mathrm{4}} \\ $$$$\mathrm{LCM}=\mathrm{140}×\mathrm{a}^{\mathrm{5}} ×\mathrm{a}^{\mathrm{4}} \\ $$

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