Amos counts out loud by six beginning with $0.$ Sarah counts out loud by three also beginning with $0.$ Between $0$ and $100$ inclusive, how many of the numbers do both Sarah and Amos say out loud?
Both Sarah and Amos say 0.
Sarah says all multiples of 3, and Amos says all multiples of 6 (under 100), because 6 is a multiple of 3 (3 x 2), then all the numbers Amos says, Sarah will say too. So now the problem becomes how many multiples of 6 are under 100?
The largest multiple of 6 under 100 is 96 (6 x 16), and the smallest would be 6 (6 x 1). 6 x 1 to 6 x 16 would yield 16 multiples.
So Amos says a multiple of 6 sixteen times, not including 0. Hence, 1 + 16 = 17 numbers that both Sarah and Amos say out loud.
Both Sarah and Amos say 0.
Sarah says all multiples of 3, and Amos says all multiples of 6 (under 100), because 6 is a multiple of 3 (3 x 2), then all the numbers Amos says, Sarah will say too. So now the problem becomes how many multiples of 6 are under 100?
The largest multiple of 6 under 100 is 96 (6 x 16), and the smallest would be 6 (6 x 1). 6 x 1 to 6 x 16 would yield 16 multiples.
So Amos says a multiple of 6 sixteen times, not including 0. Hence, 1 + 16 = 17 numbers that both Sarah and Amos say out loud.