First LCM of 20,25,35 and 40, using prime factorization method20=2×2×525=5×535=5×740=2×2×2×5LCM (20,25,35,40)=1400as per given statement we have to find the greatest number which when divided by 20,25,35 and 40 leaves remainder as 14,19,29 and 34 respectively.i.e. less than Divisor in each case .Required number =1400−6=1394......................(20−14=25−19=35−29=40−34=6) 1394 is the required number.