MathematicsFind the HCF and LCM of 288, 360 and 384 by prime factorisation method.

Find the HCF and LCM of 288, 360 and 384 by prime factorisation method.


  1. A
    LCM = 5760 and HCF = 24
  2. B
    LCM = 5551 and HCF = 24
  3. C
    LCM = 5412 and HCF = 20
  4. D
    LCM = 5789 and HCF = 23 

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    Solution:

    Given are three numbers 288, 360 and 384.
    The prime factors of a given number 288 is,
    ⇒288=2×2×2×2×2×3×3  
    The prime factors of a given number 384 is,
    ⇒384=2×2×2×2×2×2×2×3  
    The prime factors of a given number 360 is,
    ⇒360=2×2×2×3×3×5  
    Thus, the LCM of the numbers is,
    ⇒LCM=2×2×2×2×2×2×2×3×3×5 ⇒LCM=128×9×5 ⇒LCM=5760  
    Thus, the HCF of the numbers is,
    ⇒HCF=2×2×2×3 ⇒HCF=8×3 ⇒HCF=24  
    The LCM and HCF of the numbers are 5760 and 24 respectively.
    Therefore the correct answer is option (1).
     
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