InterviewSolution
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InterviewSolution
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Find the LCM and HCF of the following pairs of integer and verify that LCM×HCF=Product of the two numbers. i) 26 and 91 ii) 510 and 92 iii) 336 and 54 |
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Answer» Solution : i) 26 and 91 26=2×13×1(expressing as product of it’s prime factors) 91=7×13×1(expressing as product of it’s prime factors) So, LCM(26,91)=2×7×13×1=182 HCF(26,91)=13×1=13 Verification: LCM×HCF=13×182=2366 Product of 26 and 91 =2366 Therefore,LCM×HCF=Product of the two numbers . i) 510 and 92 510=2×3×17×5×1(expressing as product of it’s prime factors) 92=2×2×23×1(expressing as product of it’s prime factors) So, LCM(510,92)=2×2×3×5×17×23=23,460 HCF(510,92)=2 Verification: LCM×HCF=23,460×2=46,920 Product of 510 and 92 =46,920 Therefore,LCM×HCF=Product of the two numbers . iii) 336 and 54 336=2×2×2×2×7×3×1(expressing as product of it’s prime factors) 54=2×3×3×3×1(expressing as product of it’s prime factors) So, LCM(336,54)=24×33×7=3024 HCF(336,54)=2×3=6 Verification: LCM×HCF=3024×6=18,144 Product of 336 and 54=18,144 Therefore,LCM×HCF=Product of the two numbers . |
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