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Question

Determine the smallest 3-digit number which is exactly divisible by 6,8,and12.


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Solution

Smallest three digits number.

First, we have to find the LCM of 6,8,and12.

Multiples of 6,8,and12 are,

Common Multiples of 66,12,18,24,30,36,42..

Common Multiples of 88,16,24,32,40,48,54

Common Multiples of 1212,24,36,48,60,72,

It is observed that, 24 is the least common multiple.

Thus, all the multiples of 24 will also be divisible by 6,8,and12.

Now we will divide the smallest 3-digit number with the LCM obtained, and the remainder will be subtracted from the dividend, and 24 will be added to it to make it perfectly divisible.

10024=4,Remainder=4

According to the above statement.

=(1004)+24=96+24=120

Hence, the smallest 3-digit number which is exactly divisible by 6,8,and12 is 120.


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