What is the smallest number whose double is divisible by 12, 18, 21, and 30?
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Answer: B. 630
Explanation
The least common multiple of twelve, eighteen, twenty-one, and thirty is calculated as twelve hundred sixty. The problem states that the double of the required number equals this least common multiple. Dividing twelve hundred sixty by two yields the final smallest number value of six hundred thirty. The least common multiple is the smallest positive integer that is divisible by every number in a given set. Prime factorization is commonly used to find the least common multiple of large numbers efficiently. Reversing multiplier operations requires dividing the resulting common multiple by the specified factor.
Scheduling recurring maintenance events often relies on finding least common multiples of time intervals. Gear ratio designs in mechanical engineering utilize least common multiples to align teeth positions. Synchronizing flashing indicator lights involves calculating common time intervals using least common multiples. Option A represents an incorrect calculation that is not divisible by all the specified numbers. Option C represents the least common multiple itself rather than the required halved number. Option D represents double the least common multiple rather than the correct target value.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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