What is the smallest number which, when divided by 16, 18, and 21, leaves remainders of 3, 5, and 8 respectively___________?
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Answer: D. 995
Explanation
The least common multiple of divisors sixteen, eighteen, and twenty one is calculated as one thousand eight. Each divisor leaves a remainder that maintains a consistent difference of thirteen with the divisor. Subtracting this common difference of thirteen from the LCM yields the target number nine hundred ninety five. Remainder problems involving multiple divisors are solved by finding the LCM and adjusting for differences. A constant difference between divisors and their respective remainders simplifies finding the required number. The LCM represents the smallest positive integer divisible by all given divisor values.
Modular arithmetic problems model periodic scheduling and cyclical synchronization phenomena. Cryptographic algorithms rely heavily on prime factorization and remainder calculations for security. Understanding divisibility rules helps in advanced number theory and computational mathematics. Option A suggests nine hundred eighty two which does not satisfy all specified remainder conditions. Option B suggests eight hundred ninety three which fails the LCM divisor verification checks. Option C suggests one thousand twenty four which is larger than the adjusted LCM base value.
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- Mathematics
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- Mathematics
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