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

Answer:

To find the smallest 3-digit number that is divisible by 6, 8, and 12, we need to find the least common multiple (LCM) of these three numbers.

Finding the LCM:
To find the LCM, we can list the multiples of each number and find the smallest number that appears in all three lists. Let's break down the process for each number:

For 6:
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...

For 8:
The multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...

For 12:
The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, ...

Finding the smallest number in common:
From the above lists, we can see that the smallest number that appears in all three lists is 24.

Therefore, the LCM of 6, 8, and 12 is 24.

Finding the smallest 3-digit number:
To find the smallest 3-digit number (100-199) that is divisible by 24, we can divide each number in this range by 24 and check if the remainder is zero.

By dividing 100 by 24, we get a remainder of 4.
By dividing 101 by 24, we get a remainder of 5.
By dividing 102 by 24, we get a remainder of 6.
...

Continuing this process, we find that 120 is the smallest 3-digit number that is divisible by 24.

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

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