MathematicsFind the HCF and LCM of 90 and 144 by prime factorization method


Find the HCF and LCM of 90 and 144 by prime factorization method



  1. A
      630
  2. B
      549
  3. C
    345
  4. D
    720
     

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    Solution:

    Using the factor tree for the prime factorization of 90 and 144.
    We have,

    To find the HCF, we list the common prime factor and their smallest exponents in 90 and 144 as under:
    Common prime factor = 2, 3
    Least exponents that is the least amount of power we have = 1, 2
    HCF =  = 9 x 2 = 18
    To find LCM we have to make a list of all prime factors of 90 and 144, their greatest exponents as follows:
    Prime factor of 90 and 144 = 2, 3, 5
    Greatest exponents = 4, 2, 1
    LCM = 
    LCM = 720
    So, the Ans is HCF = 18 and LCM = 720.
    Hence, option 4 is correct.
     
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