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Question Number 93209 by Rasheed.Sindhi last updated on 11/May/20

Commented by Rasheed.Sindhi last updated on 12/May/20

$$\mathcal{X}cellentAproachSir!$$

Commented by Rasheed.Sindhi last updated on 12/May/20

$$WelcomeSirprakashjain!$$$$Haveseenyouinthefotumafter$$$$longtime!$$$${You}^{\prime }reoneofthosefromwhich$$$$I^{\prime }velearntalot!$$

Commented by prakash jain last updated on 11/May/20

$$\mathrm{number}\mathrm{be}14a,14b,14c$$$$a+b+c=29$$$$\mathrm{LCM}(a,b,c)=60$$$$\mathrm{Factors}\mathrm{of}60$$$$1,2,3,4,5,6,10,12,15,20,30,60$$$$\mathrm{We}\mathrm{need}\mathrm{to}\mathrm{three}\mathrm{number}\mathrm{such}$$$$\mathrm{tbat}\mathrm{sum}a+b+c=29$$$$\mathrm{GCD}(a,b,c)=1$$$$20,6,3$$$$20,5,4$$$$15,12,2$$$$15,10,4$$$$\mathrm{numbers}\mathrm{are}14a,14b,14c$$

Commented by prakash jain last updated on 11/May/20

$$\mathrm{Four}\mathrm{possible}\mathrm{choices}$$

Commented by prakash jain last updated on 12/May/20

$$\mathrm{Hi}\mathrm{Rasheed},$$$$\mathrm{Good}\mathrm{to}\mathrm{be}\mathrm{able}\mathrm{to}\mathrm{talk}\mathrm{to}\mathrm{you}\mathrm{again}.$$$$\mathrm{I}\mathrm{really}\mathrm{miss}\mathrm{lot}\mathrm{of}\mathrm{discussion}\mathrm{that}\mathrm{we}\mathrm{has}$$$$\mathrm{a}\mathrm{few}\mathrm{years}.$$$$\mathrm{I}\mathrm{was}\mathrm{just}\mathrm{now}\mathrm{scrolling}\mathrm{thru}\mathrm{our}$$$$\mathrm{old}\mathrm{discussions}\mathrm{in}\mathrm{functional}$$$$\mathrm{equations},\mathrm{number}\mathrm{theory}\mathrm{and}\mathrm{our}$$$$\mathrm{monthly}\mathrm{focus}\mathrm{topics}.$$$$\mathrm{I}\mathrm{even}\mathrm{found}\mathrm{and}\mathrm{answer}\mathrm{to}\mathrm{most}$$$$\mathrm{recent}\mathrm{question}\mathrm{in}\mathrm{Q}119.$$

Commented by Rasheed.Sindhi last updated on 12/May/20

$$Sir,alongwithyouIalsoremember$$$$someothernames:Yozii,123456,$$$$Mr.flipusandmanyothersand$$$$wishthatIcouldcontactthem!$$

Answered by mr W last updated on 11/May/20

$$hirasheedsir!$$$$niceto‘‘{see}^{″}youagain!$$$$$$$$thisismytry:$$$$LCM(a,b,c)=840=2^3\times 3\times 5\times 7$$$$GCD(a,b,c)=14=2\times 7$$$$a+b+c=406$$$$$$$$a,b,c=xwhichcanbecomposedof$$$$x=(2^1,2^{1..3},2^3)\times (3^0,3^{0..1},3^1)\times (5^0,5^{0..1},5^1)\times 7$$$$or$$$$x=(2,2..8,8)\times (1,1..3,3)\times (1,1..5,5)\times 7$$$$wecanform5\times 4\times 4\times 1=80triples.$$$$someofthemhavethesum406.$$$$onepossibilityisforexample$$$$a=8\times 1\times 1\times 7=56$$$$b=4\times 1\times 5\times 7=140$$$$c=2\times 3\times 5\times 7=210$$$$anotherpossibilityisforexample$$$$a=2\times 3\times 1\times 7=42$$$$b=4\times 3\times 1\times 7=84$$$$c=8\times 1\times 5\times 7=280$$$$......$$

Commented by Rasheed.Sindhi last updated on 12/May/20

$$\mathcal{V}.\mathcal{N}iceapproachSir!$$

Commented by Rasheed.Sindhi last updated on 12/May/20

$$Ialwaysbehappytoseeyour$$$$postssir.AlthoughI{don}^{\prime }tunderstand$$$$manyofthem.Andreallybevery$$$$happytoknowthatyoualsoremember$$$$me!$$

Commented by mr W last updated on 12/May/20

$$thankssir!certainlyirememberyou$$$$sir.tomeyouaresomeonewho$$$$alwaystriestosolveaquestionina$$$$waywithmuchanddeepthinking,$$$$evenwhenitisnotalwaysasuccess.$$$$thisinspiritsverymuch.somehow$$$$ialsotrytosolveaquestion$$$$intensionallyinawaywhichother$$$$peoplemaynottake.itisnotalways$$$$thebestway,butitmakesmorefun.$$

Commented by Rasheed.Sindhi last updated on 18/May/20

$$7hank5sira⌞⊚\mathrm{\top }!$$

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