Find the smallest number which leaves a remainder of 3 when divided by 8, 12, and 16_______?
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Answer: D. 51
Explanation
The lowest common multiple of eight, twelve, and sixteen must be determined first to solve the problem. The lowest common multiple of these three numbers is calculated to be forty eight. Adding the required remainder of three to forty eight yields the smallest target number of fifty one. The lowest common multiple is the smallest positive integer that is a multiple of all given divisors. Numbers leaving a constant remainder when divided by multiple divisors are found by adding that remainder to the LCM. Divisibility rules help verify whether candidate numbers satisfy all given conditions.
Scheduling and cyclic event planning often rely on lowest common multiple calculations. Number theory problems use remainder properties to test analytical problem solving skills. Computer science applications involve LCM concepts when synchronizing periodic software routines. Option A is incorrect because seventy one does not leave the correct remainder when divided. Option B represents a number that is not divisible by the required factors with a remainder of three. Option C is too low and fails to meet the divisibility requirements for sixteen.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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