What is the smallest number which, when increased by 1, is completely divisible by 12, 18, 24, 32, and 40__________?
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Answer: A. 1439
Explanation
Finding the least common multiple of all specified divisors determines the base number divisible by them. The least common multiple of twelve, eighteen, twenty-four, thirty-two, and forty equals one thousand four hundred forty. Subtracting one from the least common multiple gives fourteen thirty-nine, which leaves a remainder when divided. Least common multiple calculations find the smallest integer divisible by a given set of numbers simultaneously. Number theory problems involving numbers increased or decreased by constants use LCM as a foundational base. Prime factorization methods provide an efficient way to compute least common multiples for large number sets.
Production schedulers align manufacturing shift cycles using least common multiple calculations for machinery intervals. Network engineers synchronize data packet transmission intervals using least common multiple timing frequencies. Astronomers calculate planetary orbital conjunction periods using least common multiple time calculations. Option B suggests fourteen forty which is the exact LCM and would yield zero remainder when divided. Option C suggests fourteen fifty-nine which is greater than the LCM and does not satisfy divisor rules. Option D suggests fourteen forty-nine which represents an arithmetic calculation error from the LCM base.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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