Question

Is it possible for the HCF and LCM of two number to be 18 and 378 respectively ? Justify !! - Guys , Easy solution , please :-)

Answer 1

The check is done easily without finding then numbers.  Since,  LCM is a multiple of HCF, ie., 378 = 21 * 18,  the answer is yes. 

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Let the numbers be    A and B.
product of two numbers = product of LCM and HCF.
        A * B = 18 * 378
 
  let   A = 18 * M          and B = 18 * N
         A*B = 18 * 18 * M * N    = 18 * 378 = 18 * 18 * 3 * 7 * 1

There are two combinations of numbers for which this is true:
     18,  378.    and              54 , 126

Answer 2

You should know that HCF of two numbers is always a factor of the LCM.

(Why this happens is: HCF is a factor of both the numbers. Both the numbers are factors of LCM. Thus HCF is also a factor of LCM and it is always true.)


Your answer:
Check whether 18 is a factor of 378.
378 ÷ 18 = 21, remainder = 0

Since remainder is 0, 18 is a factor of 378. So It is possible for the HCF and LCM of two number to be 18 and 378 respectively