QHow many numbers between 100 and 600 are divisible by 2, 3, and 7 simultaneously?
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Explanation
To find the number of numbers between 100 and 600 that are divisible by 2, 3, and 7 simultaneously, we can first find the least common multiple (LCM) of 2, 3, and 7. The LCM of 2, 3, and 7 is 42, which means that any number that is divisible by 2, 3, and 7 must also be divisible by 42.
We can then count the number of multiples of 42 between 100 and 600. The first multiple of 42 greater than or equal to 100 is 105, and the last multiple of 42 less than or equal to 600 is 588. The number of multiples of 42 between these two numbers is:
(588 - 105) / 42 + 1 = 12
Therefore, there are 12 numbers between 100 and 600 that are divisible by 2, 3, and 7 simultaneously.
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