What is the smallest number to add to 2497 so the sum is completely divisible by 5, 6, 4, and 3:
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Answer: C. 23
Explanation
The least common multiple of five, six, four, and three is calculated to be exactly sixty. Dividing two thousand four hundred ninety-seven by sixty leaves an arithmetic remainder of thirty-seven. Subtracting thirty-seven from sixty reveals that adding twenty-three makes the resulting sum perfectly divisible by sixty. The least common multiple is the smallest positive integer that is evenly divisible by all numbers in a given set. Modular arithmetic uses remainders to determine divisibility rules and solve cyclic grouping problems. Adding a specific remainder adjustment ensures numbers align perfectly with required factor boundaries.
Option A adds three, which leaves the sum unaligned with the required least common multiple threshold. Option B adds thirteen, failing to bridge the gap required to reach the next multiple of sixty. Option D adds thirty-three, overshooting the precise adjustment needed to achieve complete divisibility.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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