What is the smallest number which, when increased by 3, is exactly divisible by 8, 12, and 18_______?
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Answer: C. 69
Explanation
The least common multiple of eight, twelve, and eighteen is calculated as seventy two. The problem states that the target number increased by three equals this least common multiple. Subtracting three from seventy two yields the final required number of sixty nine. The least common multiple is the smallest positive integer that is divisible by every number in a set. Word problems often require translating verbal conditions into inverse arithmetic operations. Divisibility rules help verify whether candidate numbers satisfy multiple factor constraints.
Common multiple problems appear frequently in synchronization and periodic event scheduling. Mathematical puzzles train students to break down multi step verbal instructions logically. Number theory applications extend to gear ratios, music rhythms, and calendar alignments. Option a gives seventy one which leaves an incorrect remainder when divided by the factors. Option b suggests seventy which does not satisfy the three unit offset condition. Option d provides sixty eight which fails to meet the required divisibility criteria.
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