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Question Number 34358 by Rasheed.Sindhi last updated on 05/May/18

$$\mathrm{Determine}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{pairs}\mathrm{whose}$$ $$\mathrm{LCM}\mathrm{is}144\mathrm{in}\mathrm{case},$$ $$\left(\mathrm{i}\right)\mathrm{when}(\mathrm{a},\mathrm{b})\mathrm{\&}(\mathrm{b},\mathrm{a})\mathrm{are}\mathrm{considered}\mathrm{same}.$$ $$\left(\mathrm{ii}\right)\mathrm{when}(\mathrm{a},\mathrm{b})\mathrm{\&}(\mathrm{b},\mathrm{a})\mathrm{are}\mathrm{considered}\mathrm{different}.$$

Commented bycandre last updated on 05/May/18

$$144=72\times 2=36\times 2^2=18\times 2^3=9\times 2^4=2^4\times 3^2$$ $$S=\{x\in \mathbb{N};x\mid 144\}$$ $$S=\{1,2,3,4,6,8,9,12,16,18,24,36,48,72,144\}$$ $$\mid S\mid =5\times 3=15$$ $$\left[\begin{array}{ccc}1& 3& 9\\ 2& 6& 18\\ 4& 12& 36\\ 8& 24& 72\\ 16& 48& 144\end{array}\right]$$

Answered by MJS last updated on 05/May/18

$$(1;144)$$ $$(2;144)$$ $$(3;144)$$ $$(4;144)$$ $$(6;144)$$ $$(8;144)$$ $$(9;144)(9;16)(9;48)$$ $$(12;144)$$ $$(16;144)(16;18)(16;36)(16;72)$$ $$(18;144)(18;48)$$ $$(24;144)$$ $$(36;144)(36;48)$$ $$(48;144)(48;72)$$ $$(72;144)$$ $$(144;144)$$ $$$$ $$\left(\mathrm{i}\right)23$$ $$\left(\mathrm{ii}\right)45$$

Commented byRasheed.Sindhi last updated on 05/May/18

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