Which is the smallest number divisible by 2, 4, and 6?

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Solution

The number exactly divisible by 2, 4, and 6 is the LCM of 2, 4, and 6.

Now,
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
Multiples of 6: 6, 12, 18, 24, 30, ...

The common multiples of 2, 4, and 6 are 12 and 24.
As 12 is the smallest common multiple, it is the LCM of 2, 4, and 6.

Thus, 12 is the smallest number exactly divisible by 2, 4, and 6.

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