+1475 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?
+1632 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.
+1632 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.
