Final answer:
To find the number of integers from 1 to 10000 (inclusive) divisible by 13 or 51, add the number of multiples of each and subtract the doubly counted multiples of their LCM. There are 769 multiples of 13, 196 multiples of 51, and 15 multiples of both, leading to a total of 950 such numbers.
Step-by-step explanation:
The question asks us to find the number of integers from 1 to 10000 (inclusive) which are divisible by either 13 or 51. To solve this problem, we need to find the count of multiples of 13, the count of multiples of 51, and subtract the count of numbers which are multiples of both (since they are counted twice). The count of multiples of a number x within a range from 1 to n can be calculated by n/x.
To find the number of multiples of 13 up to 10000, we calculate 10000/13 which gives us 769. To find the multiples of 51, we calculate 10000/51 which gives us 196. However, since 13 and 51 have a common factor, some numbers are multiples of both. Specifically, they are multiples of the least common multiple (LCM) of 13 and 51, which is 663. To find these, we calculate 10000/663, giving us 15 multiples that have been double-counted.
Therefore, the total number of integers from 1 to 10000 (inclusive) that are divisible by either 13 or 51 is 769 + 196 - 15, which equals 950.