Question

if LCM and HCF of two numbers are 288 and 9 , then the difference of both the numbers is divisible by
(1) 39 (2) 29 (3) 27 (4) 31​

Answer 1

Product of Two Numbers X*Y = HCF * LCM. You see there are 4 variables Viz. X, Y, HCF and LCM. When HCF and LCM is given, we have 2 variables (X and Y) and only one equation i. e. X * Y = HCF * LCM.

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Answer 2

given LCM and HCF of two numbers, find the number divisible by the difference of said numbers.

Explanation:

1. let the numbers be $9x$ and $9y$ (x and y are co-primes) and there HCF and LCM be h and y respectively. then HCF and LCM of two numbers are related to each other as well as with the given numbers as, $81xy=hl$
2. hence we have , $h=9\ \ \ l=288$                                                                                            therefore,    $xy=32$      $->xy=2^5$                            
3. since x and y are co-primes the only possible combinations are ,                              $xy=1x32=32x1$          
4. hence, possible difference of both numbers is $31$. hence, the answer is option $(4)$