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Quantitative Aptitude > Learn Quantitative Aptitude > If the sum of two numbers & their LCM is 79.Then how...
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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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Mentor - GMAT | CAT | IIT alum

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...
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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=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
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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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QT & DI is now a cake walk.

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...
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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 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...
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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 sujoy, You are right , however i interpreted the sum of two numbers and its lcm to be the same number(ie 79) ,which led to wrong answer. but Mukesh has replied to my answer (which has another interesting mathematical problem) can you check if any other number satisfies the mathematical problem(equations) qiven by Mukesh ----------------------------------------------------------------------------------------------------- Hi Mukesh The question must be stated as below(as per your reply) Q the sum of two numbers & its lcm be equal to concatenation of two numbers then list the set of such numbers for ex lcm of 7,9 is 63 ----1 7 +9 =16 -----2 adding 1 & 2 we get 1 eq + 2 eq = 79 ----3 3 equations equals the 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 does fractions satisfy the solutions to mathematical problem stated by Sujoy or Mukesh or both Thanks & Regards Sathya Narayanan K read less
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QT & DI is now a cake walk.

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

Interesting question and nicely answered by Sujoy.
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3 such pairs are possible 7,9; 15,4; and 19,3
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