Question

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

Answer 1

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 .