Question

Find the LCM and HCF of 144 and 198 and verify that LCM X HCF = Product of two numbers.

Answer 1

144=2×2×2×2×3×3
198=2×3×3×11


LCM(144,198)=Product of greatest power of each factor
=2^4×3^2×11
=1,584

HCF(144,198)=Product of lowest power of each common factor
=2×3×3
=18



LCM×HCF
=1,584×18
=28,512

Product of the two numbers
144×198
=28,512


Hence,verified thatLCM×HCF=Product of the two numbers

Answer 2

HCF is a largest number that “divides exactly into two or more numbers”.

LCM is two numbers is the “smallest number that they both divide evenly into”.

198 = 2×3×3×11

144 = 2×2×2×2×3×3

H C F = 2×3×3= 18

L C M = 2×2×2×11×3×3×5=1584

HCF × LCM = Products

18×1584 = 144×198

=> 28512 = 28512

hence, proved.

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