what is the least number that must be added to 2000so that the sum is devided exactly by 10,12,16 and 18

Answer:Number must be added = 160Step-by-step explanation:First we need to find LCM of 10,12,16 and 18.LCM of 10,12,16 and 18 = 720Let us write the multiplication table of 720       720, 1440, 2160, 2880 .................We need to find the least number that must be added to 2000 so that the sum is divided exactly by 10,12,16 and 18 .The number greater than 2000 is 2160.Difference = 2160 - 2000 = 160Number must be added = 160

10 = 2.5  ; 12 = 2².3 ; 126 = 2^4 ; 18 = 2.3²the least common multiple is 2^4.5.3 = 240then we have (2000 + x) = 240.k2000 = 240.8 + 80 and 240.9 = 2160then x = 160