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# If the sum of two numbers & their LCM is 79.Then how many possible set of numbers can satisfy above equation.

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Hi Sathya - there are a set of solutions - Let the numbers be A and B and their LCM be L and HCF be H. Thus, A and B are multiples of H. Let A=H*p; B=H*q. Thus, L=H*p*q; where p and q are co-prime. Hence, H*p + H*q + H*p*q = 79=> H(p + q + pq) = 79 Since 79 is prime, H = 1 and p + q + pq... read more
Hi Sathya - there are a set of solutions - Let the numbers be A and B and their LCM be L and HCF be H. Thus, A and B are multiples of H. Let A=H*p; B=H*q. Thus, L=H*p*q; where p and q are co-prime. Hence, H*p + H*q + H*p*q = 79=> H(p + q + pq) = 79 Since 79 is prime, H=1 and p + q + pq=79 add 1 to both sides: 1 + p + q + pq=80 => (p + 1)(q + 1) = 80 the solutions are: p+1 = 2, q+1 = 40=> p=1, q=39 => A=1, B=39, L=39 p+1 = 4, q+1 = 20=> p=3, q=19 => A=3, B=19, L=57 p+1 = 5, q+1 = 16=> p=4, q=15 => A=4, B=15, L=60 p+1 = 8, q+1 = 10=> p=7, q=9 => A = 7, B = 9, L = 63 Thus, there are 4 pairs. :) read less

Concatenation of the two numbers 7 & 9. Can you please check and tell if any other number satisfy the mathematical problem(equations) qiven by Sujoy ------------------------------------------------------------ Hi Srikanth, Please can you tell me -

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Only 3 such pairs exist (7,9) (4,15) (19,3) only.

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Hi No set of values satisfy both the equations. 79 is a prime number. the factors of 79 are 1,79 LCM of 79,79 is 79 but its sum is 79+79=158 LCM of 79,158 is 79 but its sum is 79+158=237 If two numbers has LCM as 79 then its sum is not 79 but will be alteast 158 lets say LCM a, b... read more
Hi No set of values satisfy both the equations. 79 is a prime number. the factors of 79 are 1,79 LCM of 79,79 is 79 but its sum is 79+79=158 LCM of 79,158 is 79 but its sum is 79+158=237 If two numbers has LCM as 79 then its sum is not 79 but will be alteast 158 lets say LCM a, b is 79 then both a,b are multiples of 79 (minimum value of both a & b is 79) the minimum value of a+b is 158(a=b=79) a=79,b=79,158 a+b =158+79=3*79 LCM of 79,158 is 79 a=79,b=474 LCM of 79,474 is 79. 79+474 is 553 Thus no set of values will satisfy both the equations However there infinitely many values for each of the equations. The sum of infinite set of values give 79 like 45+34, 80+-1(80,-1) ans so on. Also LCM of 79,a*79 is 79 where a is non-zero positive number Thanks & Regards Sathya Narayanan K read less

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Hi Sujoy & Mukesh, I thank both of you for your reply and answering the questions briefly. The questions you have answered varies only slightly. The answer to the third variation is given by me(even though wrongly answered according to the question). ------------------------------------------------------------ hi... read more

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NET/SLET/SET shall remain the minimum eligibility condition for recruitment and appointment of Assistant Professors in Universities/Colleges/Institutions. Provided however, that candidates, who are or have been awarded a Ph. D. Degree in accordance with the University Grants Commission (Minimum Standards and Procedure for Award of Ph.D read less

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Sathya, I appreciate your efforts to throw light on my question..but its not necessary to be such pairs as prime but yes it has to be coprime. As you can see that only 3 pairs (7,9) (4,15) & (19,3) exist...lets take example of (7,9)..the addition of both numbers is 16 & their LCM is 63 so if you add... read more
Sathya, I appreciate your efforts to throw light on my question..but its not necessary to be such pairs as prime but yes it has to be coprime. As you can see that only 3 pairs (7,9) (4,15) & (19,3) exist...lets take example of (7,9)..the addition of both numbers is 16 & their LCM is 63 so if you add 16 & 63 you will get 79 as your answer which satisfy above equation..for rest two you can also check at your own & you will get the same answer.. read less

Correctly answered Mukesh .. 3 such pairs are possible 7,9; 15,4; and 19,3

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Interesting question and nicely answered by Sujoy.

3 such pairs are possible 7,9; 15,4; and 19,3

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