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

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

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

$$\overline{)\begin{array}{cccc}abc& 14a^2{b}^3{c}^4& 20{ab}^4{c}^4& 35a^5{b}^{3}c\\ b^2& 14{ab}^2{c}^3& 20b^3{c}^3& 35a^4{b}^2\\ b& 14{ac}^3& 20{bc}^3& 35a^4\\ c^3& 14{ac}^3& 20c^3& 35a^4\\ a& 14a& 20& 35a^4\\ a^3& 14& 20& 35a^3\\ 7& 14& 20& 35\\ 5& 2& 20& 5\\ 2& 2& 4& 1\\ 2& 1& 2& 1\\ & 1& 1& 1\end{array}}$$$$L.C.M=abc\times b^2\times b\times c^3\times a\times a^3\times 7\times 5\times 2\times 2$$$$=140a^5{b}^4{c}^4$$

Commented by Spillover last updated on 11/Oct/22

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

Answered by Spillover last updated on 11/Oct/22

$$14,2035\mathrm{LCM}=140$$$${\mathrm{a}}^2\mathrm{a}{\mathrm{a}}^5\mathrm{LCM}={\mathrm{a}}^5$$$${\mathrm{c}}^4,{\mathrm{c}}^3\mathrm{c}\mathrm{LCM}={\mathrm{c}}^4$$$$\mathrm{LCM}=140\times {\mathrm{a}}^5\times {\mathrm{a}}^4$$

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