Determine the greatest 3 digit number exactly divisible by 8, 10, and 12.

Given :

The given numbers are 8, 10, 12.

To do :

We have to find the greatest three-digit number exactly divisible by the given numbers.

Solution :

The greatest 3 digit number exactly divisible by 8, 10 and 12 will be a multiple of the LCM of 8,10 and 12.

LCM of 8,10 and 12 is,

$8 = 2\times2\times2$

$10 = 2\times5$

$12 = 2\times2\times3$

LCM $= 2\times2\times2\times5\times3 = 120$.

Multiples of 120 are 120, 240, 360, 480, 600, 720, 840, 960, 1080....

Therefore,

The greatest 3 digit number exactly divisible by 8, 10 and 12 is 960.