Question

find the greatest 3-digit number exactly divsible by 8,10 and 12

Answer 1

The greatest 3 digit number which is exactly divisible by 8, 10 and 12 is 960.
 
The method for finding this is given below.

The Least Common Multiple of 8, 10 and 12 is 120. However, this is the smallest 3 digit multiple of 8, 10 and 12.

If we keep finding additional 3 digit numbers that are divisible by 8, 10 and 12 we find that they are generally multiples of 12.

So, all multiples from 120 are

120, 240, 360, 480, 600, 720, 840, 960, 1080 and 1200. The greatest 3 digit multiple of 8, 10 and 12 will be 960.

This is how you get 960 as the correct answer.

Answer 2

The greatest 3 digit number divisible by 8,10 and 12 =?
STEP 1 :Find the LCM of the three numbers.
               LCM of 8,10 and 12 = 120
STEP 2 : Now, the 120 is the smallest 3 digit number divisible by 8,10 and 12
                So,now do the multiplication table of 120
                120,240,360,480,600,720,840960,1080 ...
STEP 3    Now the greatest 3 digit number was 960 

Therefore, 960 is the greatest 3 digit number exactly divisible by 8,10 and   12