SOLUTION: What is the least number that must be added to 2000 so that the sum is divisible exactly by 10,12,16 and 18?

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Question 1090940: What is the least number that must be added to 2000 so that
the sum is divisible exactly by 10,12,16 and 18?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
What is the least number that must be added to 2000 so that
the sum is divisible exactly by 10,12,16 and 18?
The integers divisible by any set of positive 
integers are the multiples of their LCM

 10 = 2          ×5
 12 = 2×2    ×3
 16 = 2×2×2×2
 18 = 2      ×3×3 
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.

We want to know  the least number that must be added to 2000
that will give 2160.

Answer 2160-2000 = 160

Edwin
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