Find the HCF and LCM of 144, 180 and 192 by prime factorization method

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12 and 2880

32 and 1235

12 and 1267

68 and 3465

answer is A.

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Detailed Solution

Using the factor tree for the prime factorization of 144, 180 and 192, we have
Question Image

To find the HCF, we list the common prime factor and their smallest exponents in 144, 180 and 192 follows:
Common prime factor                          Least
Exponents
      2                                                        2
      3                                                        1

To find the LCM, we list all prime factors of 144, 180, 192 and their greatest
Prime factors of 144, 180 and 192
Greatest exponents
6                           2
2                           3
1                           5
Question Image

Hence, option 1 is correct.

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