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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.

HCF of 96 and 404 is 4

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