What is the largest five-digit integer that is evenly divisible by 32, 36, 40, 42, and 48_________?
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Answer: D. 90720
Explanation
The least common multiple of all the given divisor numbers is calculated as fifty zero forty. Dividing the largest five digit number by this least common multiple identifies the scaling multiplier. Multiplying the least common multiple by the integer quotient yields ninety thousand seven hundred twenty. A number divisible by multiple divisors must be a multiple of their least common multiple. The largest five digit integer in our standard decimal numbering system is ninety nine thousand nine hundred ninety nine. Finding divisibility involves integer division and multiplication to scale within digit limits.
Number theory and divisibility rules are foundational for cryptography and computer science algorithms. Scheduling problems involving repeating cycles rely on least common multiple calculations. Finding maximum constrained integers tests advanced arithmetic reasoning and number sense. Option a provides ninety thousand seven hundred thirty which is not evenly divisible by the divisors. Option b gives a number that leaves a remainder when divided by the requiredLCM value. Option c fails divisibility tests for several of the specified prime and composite factors.
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- Mathematics
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- Mathematics
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