Discussion
How many natural numbers between 1 and 500 are divisible by each of the numbers 3, 5 and 7 ?
Answer: B
There are 4 such numbers.
A number divisible by each of 3, 5 and 7 is divisible by their LCM, which is \(3 \times 5 \times 7 = 105\). The multiples of 105 below 500 are 105, 210, 315 and 420; the next, 525, exceeds 500.
\[ \left\lfloor \frac{500}{105} \right\rfloor = 4 \]
3, 5 and 6 come from miscounting the multiples.
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