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Question Number 177929 by Spillover last updated on 11/Oct/22

$$\mathrm{Find}\mathrm{LCM}$$$$3\mathrm{y}+12,{\mathrm{y}}^2-16\mathrm{and}{\mathrm{y}}^4-64\mathrm{y}$$

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

$$3\mathrm{y}+12,{\mathrm{y}}^2-16,{\mathrm{y}}^4-64\mathrm{y}$$$$\iff 3(\mathrm{y}+4),(\mathrm{y}-4)(\mathrm{y}+4),\mathrm{y}(\mathrm{y}-4)({\mathrm{y}}^2+4\mathrm{y}+16)$$$$\overline{)\begin{array}{cccc}\mathrm{y}+4& 3(\mathrm{y}+4)& (\mathrm{y}-4)(\mathrm{y}+4)& \mathrm{y}(\mathrm{y}-4)({\mathrm{y}}^2+4\mathrm{y}+16)\\ \mathrm{y}-4& 3& \mathrm{y}-4& \mathrm{y}(\mathrm{y}-4)({\mathrm{y}}^2+4\mathrm{y}+16)\\ {\mathrm{y}}^2+4\mathrm{y}+16& 3& 1& \mathrm{y}({\mathrm{y}}^2+4\mathrm{y}+16)\\ \mathrm{y}& 3& 1& \mathrm{y}\\ 3& 3& 1& 1\\ & 1& 1& 1\end{array}}$$$$L.C.M=3\mathrm{y}(\mathrm{y}-4)(\mathrm{y}+4)({\mathrm{y}}^2+4\mathrm{y}+16)$$$$=3(\mathrm{y}+4)({\mathrm{y}}^4-64\mathrm{y})$$

Commented by Spillover last updated on 11/Oct/22

$$\mathrm{thank}\mathrm{you}$$

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