Question and Answers Forum

All Questions      Topic List

Number Theory Questions

Previous in All Question      Next in All Question      

Previous in Number Theory      Next in Number Theory      

Question Number 30687 by Rasheed.Sindhi last updated on 24/Feb/18

$$\mathrm{Given}\mathrm{that}\mathrm{LCM}(\mathrm{A},\mathrm{B},\mathrm{C})=252$$ $$\mathrm{LCM}(\mathrm{A},\mathrm{B})=36\mathrm{\&}\mathrm{LCM}(\mathrm{A},\mathrm{C})=63;$$ $$\mathrm{then}:$$ $$\mathrm{LCM}(\mathrm{B},\mathrm{C})=?$$ $$\mathrm{Pl}\mathrm{determine}\mathrm{all}\mathrm{possible}\mathrm{answers}.$$

Answered by MJS last updated on 24/Feb/18

$$252=2^2{3}^{2}7$$ $$36=2^2{3}^2$$ $$63=3^{2}7$$ $$\{A,B\}=\{4,9\}\vee \{9,4\}\vee \{1,36\}\vee \{36,1\}$$ $$\{A,C\}=\{7,9\}\vee \{9,7\}\vee \{1,63\}\vee \{63,1\}$$ $$A=9$$ $$B=4$$ $$C=7$$ $$LCM(4,7)=28$$ $$\mathrm{or}$$ $$\mathrm{A}=1$$ $$B=36$$ $$C=63$$ $$LCM(36,63)=252$$

Commented byRasheed.Sindhi last updated on 24/Feb/18

$$\mathcal{T}h\alpha \eta \kappa \mathcal{S}\mathcal{S}ir!$$ $$\mathcal{A}\mathrm{re}\mathrm{other}\mathrm{answers}\mathrm{also}\mathrm{possible}?$$ $$\mathrm{Could}\mathrm{we}\mathrm{detefmine}\mathrm{all}\mathrm{possibilities}?$$

Commented byMJS last updated on 24/Feb/18

$$\mathrm{sorry},\mathrm{even}\mathrm{more}\mathrm{possibilities}:$$ $$\mathrm{if}A\mathrm{or}B=36\mathrm{the}\mathrm{other}\mathrm{one}\mathrm{can}\mathrm{be}$$ $$1,2,3,4,6,9,12,18\mathrm{or}36$$ $$\mathrm{if}A\mathrm{or}C=63\mathrm{the}\mathrm{other}\mathrm{one}\mathrm{can}\mathrm{be}$$ $$1,3,7,9,21\mathrm{or}63$$ $$\mathrm{so}\mathrm{also}\mathrm{possible}:$$ $$\{A,B,C\}=\{3,36,63\}\vee \{9,36,63\}$$ $$\mathrm{but}\mathrm{the}LCM(B,C)\mathrm{is}252\mathrm{too}$$

Commented bysoksan last updated on 25/Feb/18

$$252=2^2{3}^{2}7$$ $$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com