MathematicsState true or false.It is possible that HCF and LCM of two numbers can be 24 and 540 respectively?

State true or false.


It is possible that HCF and LCM of two numbers can be 24 and 540 respectively?


  1. A
    True
  2. B
    False 

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    Solution:

    It is required to find whether that HCF and LCM of two numbers can be 24 and 540 are possible.
    Fundamental Theorem of Arithmetic states every composite number can be expressed as a product of primes, and this factorization is unique except for the order in which the prime factors occur.
    HCF of two numbers =24  .
    LCM of two numbers =540  .
    Always a multiple of HCF is LCM. In other words, HCF totally divides LCM. Now, LCM of two numbers HCF of tw numbers = 540 24 ⇒ 45 2 ⇒22.5≠Integer  
    Hence, two numbers cannot have HCF and LCM as 24 and 540 respectively.
    Therefore, the given statement is false.
    Thus, option 2 is correct.
     

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