Question

hcf of 96 and 404 is

Answer 1

Solution : 
90 = 2 x 45 
= 2 x 3 x 15 
= 2 x 3 x 3 x 5 
90 = 2 x 3 2 x 5 
144 = 2 x 72 
= 2 x 2 x 36 
= 2 x 2 x 2 x 18 
= 2 x 2 x 2 x 2 x 9 
= 2 x 2 x 2 x 2 x 3 x 3
144 = 2 4 x 3 2 
To find the HCF, we list the common prime factors and their smallest exponents in 90 and 144 as under : 
Common factorsLeast exponents2132
∴ HCF = 2 1 x 3 2 = 2 x 9 = 18
To find the LCM, we will list all prime factors of 90 and 144 and their greatest exponents as follows : 
Prime factors of 90 and 144Greatest exponents243251∴ LCM = 2 4 x 3 2 x 5 = 16 x 9 x 5 = 720 
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2) Find the HCF of 96 and 404 by prime factorization method. Hence, find their LCM.
Solution : 
96 = 2 5 x 3 and 404 = 2 2 x 101 
∴ HCF = 2 2 = 4
⇒ LCM = (96 x 404) / HCF 
⇒ LCM = (96 x 404)/4 = 96 x 101 = 9696.