Final answer:
To find the number of integers between 100 and 999 that are divisible by either 3 or 4, use the principle of inclusion-exclusion. The final answer is 300 + 250 - 100 = 450.
Step-by-step explanation:
To find the number of integers between 100 and 999 that are divisible by either 3 or 4, we can use the principle of inclusion-exclusion. First, we find the number of integers divisible by 3, which is 300. Next, we find the number of integers divisible by 4, which is 250. However, if we simply add these two numbers together, we would be counting some integers twice. To avoid this, we need to subtract the number of integers divisible by both 3 and 4. The numbers divisible by both 3 and 4 are the multiples of the LCM of 3 and 4, which is 12. There are 100 multiples of 12 between 100 and 999. Therefore, the final answer is 300 + 250 - 100 = 450.