Determine the smallest 3-digit number which is exactly divisible by 6,8 and 12.

Given :

The given numbers are 6, 8, 12.

To do :

We have to find the smallest three digit number which is divisible by 6, 8, 12.

Solution :   

The smallest 3-digit which is exactly divisible by 6,8 and 12 will be a multiple of LCM of 6,8 and 12.

LCM of 6,8 and 12 is,

$6 = 2\times3$

$8 = 2\times2\times2$

$12 = 2\times2\times3$

$LCM = 2\times2\times2\times3 = 24$

Multiples of 24 are 24, $24\times2=48,......., 24\times5=120,.....$

Therefore, the smallest 3-digit which is exactly divisible by 6, 8 and 12 is 120. 

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Updated on: 10-Oct-2022

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