Find the sum of two numbers, which are greater than 29 and have H.C.F. and L.C.M. of 29 and 4147 respectively.

Question: Find the sum of two numbers, which are greater than 29 and have H.C.F. and L.C.M. of 29 and 4147 respectively.Solution:Product of two numbers = Product of their H.C.F. and L.C.M.Product of two numbers = 29 × 4147 = 120263Two numbers are greater than 29.Therefore, let the two numbers be 29x and 29y.So, 29x × 29y = 120263xy = 143Factors of 143 are: 1, 11, 13, and 143Case: 1) If we consider factors of 143 as 1 and 143 (co-primes), then we get the value of two numbers x and y = (29 and 4147) ------ (Which is wrong: As it is given that, the numbers are greater than 29)Case: 2) If we consider factors of 143 as 11 and 13 (co-primes), then we get the value of two numbers x and y = (319, 377) ------ (These two values are greater than 29. So, it is the correct answer)Therefore, the two numbers are 319 and 377.Sum of two numbers = 319 + 377 = 696