Determine the greatest four-digit number which is exactly divisible by 10,12,16.?

Given: 10,12,16.

To find: We have to find the greatest four-digit number which is exactly divisible by 10,12,16.

Solution:  

LCM of 10, 12, 16 = 240

We know that the greatest four-digit number is 9999.

Now, if divide 9999 by 240 we get 41 as quotient and 159 as a reminder.

So subtract 159 from 9999 to get the greatest four-digit number which is exactly divisible by 10,12,16.

9999 - 159 = 9840.

So the required number is 9840.