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

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

  1. A
    12 and 2880
  2. B
    32 and 1235
  3. C
    12 and 1267
  4. D
    68 and 3465 

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    Solution:

    Using the factor tree for the prime factorization of 144, 180 and 192, we have
    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
    Hence, option 1 is correct.
     
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