ReadBasicsofLCMandHCFHere,BeforestartingPractice

1.Findtheleastnumberwhichwhenincreasedby4isexactlydivisibleby8,16,24,30and32?a)480b)484c)476d)472e)Noneofthese

2.Whatisthegreatestnumberoffivedigitswhichwhen3769isaddedtoitwillbeexactlydivisibleby5,6,10,12,15and18?a)4309b)99459c)100539d)99911e)NoneofThese

3.Findtheminimumnumberofsquaretilesrequiredtopavethefloorofaroomof2m50cmlongand1m50cmbroad?a)50b)750c)45

d)15e)Noneofthese

4.Fivebellstolltogetherattheintervalsof5,6,8,12and20secondsrespectively.Findthenumberoftimestheytolltogetherinonehour'stime(Inclusiveofthetollatthebeginning)a)120b)31c)30d)5e)NoneofThese

5.Amilkmanhasthreedifferentkindsofmilk493liters,551litersand435liters.Findtheminimumnumberofequalsizecontainersrequiredtostoreallthemilkwithoutmixing.a)29b)51c)58d)49e)Noneofthese

6.Thecircumferenceofthefrontandbackwheelsofavehicleare63/14mand81/18mrespectively.Atanygivenmoment,achalkmarkisputonthepointofcontactofeachwheelwiththeground.Findthedistancetraveledbythevehiclesothatboththechalkmarksareagainonthegroundatthesametimea)217.5mb)435m

c)412md)419me)Noneofthese

7.TheLCMoftwonumbersis28timesoftheirHCF.ThesumoftheirLCMandHCFis1740.Ifoneofthenumbersis420,theothernumberisa)150b)225c)180d)240e)Noneofthese

8.TwopersonsAandBwalkaroundacirculartrackwhoseradiusis1.4km.Awalksataspeedof176metersperminutewhileBwalksataspeedof110metersperminute.iftheybothstartatthesametime,fromthesamepointandwalkinthesamedirection,atwhatintervaloftimewouldtheybothbeatthesamestartingpointagain?(inHours)a)62/3b)21/3c)51/4d)32/3e)Noneofthese

9.Findtheleastnumberwhichwhendividedby8,9,15,24,32and36leavesremainders3,4,10,19,27and31respectively?a)2880b)2885

c)2974d)2875e)Noneofthese

10.Findthegreatestnumberwhichwhendivide357,192and252leavessameremainderineachcasea)45b)1c)15d)Cantbedetermindee)Noneofthese

Solutions:

1.LCMof8,16,24,30and32is480So,Requirednumberis4804=476

2.LCMof5,6,10,12and18is540Ondividing(99999+3769)by540,theremainderis88So,therequirednumberis9999988=99911

3.HCFof250cmand150cmis50cm,whichisthesideofthetile

So,therequirednumberoftiles=(250X150)/(50X50)=15

4.TimeafterwhichallthebellstoltogetheristheLCMof5,6,8,12and20.i.e.,120seconds=20minutesThenumberoftimestheytolltogetherinonehour=60/2=30+1(beginningtone)So,theansweris31

5.Asminimumnumberofcontainersarerequired,thesizeofthecontainershouldbemaximumandthesizeisalsoequal.sosizeofthecontainerwillbeHCFof493,551and435i.e.,29So,requirednumberofcontainersis=(493+551+435)/29=51

6.TherequireddistanceistheLCMof63/14and81/18LCMof63/14and81/18=LCM(87/14,145/18)=>LCM(87,145)/HCF(14,18)=435/2=217.5m7.LCM=28HCFLCM+HCF=1740=>28HCF+HCF=1740HCF=1740/29=60andLCM=28X60ifaandbaretwonumbers,thenLCMof(a&b)XHCFof(a&b)=aXb28X60X60=xX420=>x=240So,theothernumberis240

8.Circumferenceofthetrackis2r=2X(22/7)X1400m=8800m

TimetakenbyAtocompleteoneround=(8800m)/(176m/min)=(8800X60)/(176)=3000sec

TimetakenbyBtocompleteoneround=(8800)/(110m/min)=(8800X60)/(110)=4800sec

TimetheymeettogetheratthestartingpointisLCMof3000and4800seci.e.,24000sec=62/3hoursSo,theymeetatthestartingpointafter62/3hours

9.Wecanobservethatthedifferencebetweenthenumbersandtheirremaindersissamei.e.,83=94=1510=2419=3227=3631=5

So,requiredanswerisLCM(8,9,15,24,32,36)5=>28805=2875

10.RequiredanswerisHCF(357192,192252,357252)=>HCF(165,60,105)=15