Question

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

Answer 1

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

Answer 2

Number must be added = 160

Explanation:

First we need to find LCM of 10,12,16 and 18.

LCM of 10,12,16 and 18 = 720

Let 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 = 160

Number must be added = 160