What is the smallest four-digit integer that can be divided without remainder by 15, 25, 40, and 75_________?
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Answer: C. 9600
Explanation
The least common multiple of fifteen, twenty five, forty, and seventy five is calculated as six hundred. Dividing the smallest four digit number by six hundred identifies the lower bounding multiplier. Multiplying six hundred by the appropriate integer factor yields the smallest four digit multiple of ninety six hundred. The smallest four digit integer in our decimal numbering system is one thousand. Any number divisible by a set of divisors must be a multiple of their least common multiple. Finding the smallest four digit multiple requires scaling the least common multiple upward.
Divisibility analysis is vital in computer science for memory allocation and periodic scheduling. Number theory problems help develop systematic approaches to finding common multiples and factors. Least common multiple calculations are used to synchronize recurring events and processes. Option a suggests nine thousand which represents a five digit threshold multiple rather than four. Option b proposes ninety four hundred which is not an exact multiple of the least common multiple. Option d gives ninety eight hundred which exceeds the smallest four digit multiple requirement.
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- Mathematics
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- Mathematics
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- Difficulty
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