Question

Find the HCF and LCM of foll. using FUNDAMENTAL THEOREM of ARITHMETIC method:
(1) 426 and 576
(2) 448, 1008 and 168

Answer 1

(1)

426 = 2 * 3 * 71

576 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 

        = 2^6 * 3^2.


Now,

LCM = 2^6 * 3^2 * 71

        = 40896.


HCF = 2 * 3

         = 6.




(2) 

448 = 2 * 2 * 2 * 2 * 2 * 2 * 7

       = 2^6 * 7


1008 = 2 * 2 * 2 * 2 * 3 * 3 * 7

         = 2^4 * 3^2 * 7


168 = 2 * 2 * 2 * 3 * 7.

       = 2^3 * 3 * 7

Now,

LCM = 2 * 2 * 2 * 7

         = 56


HCF = 2 * 2 * 2 * 7

         = 56



Hope this helps!

Answer 2

426 and 576

Fundamental Theorem of Arithmetic = prime factorization

prime factors of 426= 2*3*71

prime factors of 576= 2*2*2*2*2*2*3*3

2^6*3^2

common factors . = 2*3

hcf=2*3= 6

lcm= 2^6*3^2*71= 40896

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