How many numbers between 0 and 100 are divisible by both 6 and 8?

To find the numbers that are divisible by both 6 and 8, you first need to find their least common multiple (LCM). Think of the LCM as the smallest number that both 6 and 8 can divide into without a remainder. The multiples of 6 are 6, 12, 18, 24, and so on, while the multiples of 8 are 8, 16, 24, 32, and so on. The first number they have in common is 24. This means that any number divisible by both 6 and 8 must also be a multiple of 24.

With this "magic number" of 24 in hand, the rest is simple counting. We just need to find all the multiples of 24 that fall between 0 and 100. The first is 24 itself (24 x 1). The next is 48 (24 x 2), followed by 72 (24 x 3), and finally 96 (24 x 4). The very next multiple would be 120 (24 x 5), which is over the 100 limit. This leaves us with a total of four numbers that fit the criteria.

This mathematical principle isn't just for trivia; it has many practical uses. It's the same logic used for finding a common denominator when adding fractions or for solving scheduling problems. For example, if one bus arrives at a stop every 6 minutes and another arrives every 8 minutes, they will both arrive at the same time every 24 minutes.