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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.
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