What is the smallest four-digit integer divisible evenly by 4, 6, 8, and 10_________?
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Answer: A. 1080
Explanation
Finding the least common multiple of four, six, eight, and ten gives a base value of one hundred twenty. Dividing the smallest four-digit number one thousand by one hundred twenty gives eight point thirty-three. Multiplying one hundred twenty by the next integer multiplier nine yields the smallest four-digit multiple, ten eighty. The least common multiple is the smallest positive integer that is divisible by all numbers in a given set. Four-digit integers range strictly from one thousand up to nine thousand nine hundred ninety-nine. Finding a multiple within a specific digit range requires scaling the least common multiple by appropriate integers.
Option B is not divisible evenly by all the given factors due to a non-zero remainder. Option C is a four-digit number but fails the strict divisibility test for the given factors. Option D represents a higher multiple that is not the smallest four-digit integer satisfying the condition.
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- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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