Sir Dwayne is in charge of dragon designs at the King's Toy
Factory. He hopes that his new designs will please the king
*Your Highness," he says. "I have the plans for the toy
dragons. If it pleases you, every 3rd dragon shall billow
clouds of smoke through its nostrils. every 4th dragon shall
breathe fire, every 6th dragon shall have glowing eyes, and
every 8th dragon shall have a tail with spikes on it. i shail
make 100 dragons." The king asks. Sir Dwayne, how many
dragons shall have more than one of these
characteristics?" Sir Dwayne doesn't have the answer. Can
you help him answer the king before he is thrown into the
dungeon?

Explanation:

Any multiple of 3 and 4 shall blow clouds of smoke through its nostrils and breathe fire. Those are:

Hence, that is 8 dragons that shall have both characteristics.

Any multiple of 6 shall have glowing eyes. The common multiples of 6 and 3 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96.

Then, that adds:

Hence, add 8 more dragons.

And the common multiples of 6 and 4 are: 12, 24, 36, 48, 60, 72, 84, and 96, all of which are already included.

Any multiple of 8 shall have a tail with spikes on it. Then, you must find the common multiples of 8 and 3, 8 and 4, and 8 and 6.

Common multiples of 8 and 3 are: 24, 48, 72, and 96, which are already included.

Common multiples of 8 and 4 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, and 96. Then, you must add:

Those are other 8 dragons.

At the end the number of dragons that shall have more than one of these characteristics is:

560

hope this : )