There are 79 natural numbers till 200 that are divisible by 3 or 5.
To solve this, we use the principle of inclusion-exclusion. We find the number of multiples of 3, the number of multiples of 5, and then subtract the number of multiples of both 3 and 5 (i.e., multiples of 15) to avoid double-counting.
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Multiples of 3: The largest multiple of 3 less than or equal to 200 is 198 (3 * 66). So, there are 66 multiples of 3.
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Multiples of 5: The largest multiple of 5 less than or equal to 200 is 200 (5 * 40). So, there are 40 multiples of 5.
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Multiples of 15: The largest multiple of 15 less than or equal to 200 is 195 (15 * 13). So, there are 13 multiples of 15.
Using the principle of inclusion-exclusion:
Total = (Multiples of 3) + (Multiples of 5) - (Multiples of 15)
Total = 66 + 40 - 13
Total = 106 - 13
Total = 93
Therefore, there are 93 natural numbers up to and including 200 that are divisible by either 3 or 5.
Oops! Previous calculations were incorrect. The correct calculation is shown above.
