The number of integers divisible by both 3 and 7 depends on the range of numbers considered. A number divisible by both 3 and 7 is divisible by their least common multiple (LCM). Since 3 and 7 are prime numbers, their LCM is simply their product: 3 x 7 = 21. Therefore, we are looking for the number of multiples of 21 within a given range.
Examples and Explanations
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Reference Example 1: Between 1 and 250, there are 11 multiples of 21 (21, 42, 63, ..., 231). This reference correctly identifies 11 multiples of 21 within that specific range.
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Reference Example 2: Several references illustrate finding the number of multiples within different ranges. The approach is consistent: find the LCM (21) and then determine how many multiples of 21 fall within the specified range.
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How to Calculate: To determine the number of multiples of 21 within a range (let's say from 1 to N), you can perform the following calculation:
floor(N / 21)wherefloor()represents rounding down to the nearest whole number.- For instance, if N = 250,
floor(250 / 21) = 11. - If N = 125,
floor(125 / 21) = 5.
- For instance, if N = 250,
Different Interpretations of the Question
The original question is incomplete. To provide a precise answer, we need to know the range of numbers being considered. The question should be more specific, for example: "How many numbers between 1 and 250 are divisible by 3 and 7?"
