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How many integers between 1 and 7 000, including both 1 and 7000, are divisible by 2, 5, and 7?

Question

How many integers between 1 and 7,000, including both 1 and 7000, are divisible by 2, 5, and 7?

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Solution

To find the number of integers between 1 and 7000 that are divisible by 2, 5, and 7, we first need to find the least common multiple (LCM) of 2, 5, and 7.

Step 1: Find the LCM of 2, 5, and 7 The LCM of 2, 5, and 7 is 70.

Step 2: Find how many times 70 fits into 7000 To do this, we divide 7000 by 70. The result is 100.

So, there are 100 integers between 1 and 7000 that are divisible by 2, 5, and 7.

This problem has been solved

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