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Find L.C.M & H.C.F of 8/9 ;10/27 &16/81 . |
| Answer» {tex}\\mathrm { HCF } \\left( \\frac { 8 } { 9 } , \\frac { 10 } { 27 } , \\frac { 16 } { 81 } \\right){/tex}\xa0{tex}= \\frac { \\mathrm { HCF } \\text { of the numerators } } { \\mathrm { LCM } \\text { of the denominators } }{/tex}\xa0{tex}= \\frac { H C F ( 8,10,16 ) } { L C M ( 9,27,81 ) }{/tex}\xa0and\xa0{tex}\\operatorname { LCM } \\left( \\frac { 8 } { 9 } , \\frac { 10 } { 27 } , \\frac { 16 } { 81 } \\right){/tex}\xa0{tex}= \\frac { L C M \\text { of the numerators } } { \\text { HCF of the denominators } }{/tex}\xa0{tex}= \\frac { L C M ( 8,10,16 ) } { H C F ( 9,27,81 ) }{/tex}Consider,\xa08 = 2 {tex}\\times{/tex} 2 {tex}\\times{/tex} 2 = 2310 = 2 {tex}\\times{/tex}516 = 2 {tex}\\times{/tex} 2 {tex}\\times{/tex} 2{tex}\\times{/tex} 2 = 24So, the HCF{tex} (8, 10, 16){/tex} = 2 and LCM {tex}(8, 10, 16){/tex}\xa0{tex}= 2 ^ { 4 } \\times 5 = 80{/tex}9 = 3 {tex}\\times{/tex}3 = 3227 =3\xa0{tex}\\times{/tex} 3\xa0{tex}\\times{/tex} 3 = 3381 = 3 {tex}\\times{/tex} 3 {tex}\\times{/tex} 3 {tex}\\times{/tex} 3 = 34So, the HCF (9, 27, 81) = 32 = 9 and LCM (9, 27, 81) = 34 = 81{tex}\\Rightarrow \\text { HCF } \\left( \\frac { 8 } { 9 } , \\frac { 10 } { 27 } , \\frac { 16 } { 81 } \\right) = \\frac { 2 } { 81 }{/tex}\xa0and\xa0{tex}\\operatorname { LCM } \\left( \\frac { 8 } { 9 } , \\frac { 10 } { 27 } , \\frac { 16 } { 81 } \\right) = \\frac { 80 } { 9 }{/tex} | |