The integers divisible by any set of positive
integers are the multiples of their LCM
let us first write the factored form of each
10 = 2×5
12 = 2×2×3
16 = 2×2×2×2
18 = 2 x3×3
Now we will find lcm of these numbers
LCM = 2×2×2×2×3×3×5 = 720
The multiples of 720 are divisible by 10,12,16 and 18.
2000/720 = 2.777777...
The least integer greater than that is 3, so 3×720 = 2160 is
the least integer greater than 2000 that is divisible by
10,12,16 and 18.
so if we need to find what must be added to 2000 so that the sum is divisible by 10,12,16 and 18, we must subtract 2000 from 2160
2160-2000=160
so we must add 160 to 2000 so that the sum is divisible exactly 10,12,16and 18
