Find the smallest number which, when decreased by 7, is divisible by 21, 28, 36, and 45________?
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Answer: A. 1267
Explanation
Finding the least common multiple of twenty-one, twenty-eight, thirty-six, and forty-five yields twelve sixty. The problem states that when the desired number is decreased by seven, it becomes divisible by the LCM. Adding seven back to twelve sixty results in the final required number of twelve sixty-seven. The least common multiple of a set of divisors is the smallest number divisible by each divisor. Remainder and decrease word problems can be solved by finding the LCM and adjusting by the offset value. Adding the offset back to the LCM ensures the remainder condition is satisfied perfectly.
Divisibility puzzles appear frequently in quantitative aptitude tests to measure analytical reasoning skills. Computer scientists use modular arithmetic and least common multiples in cyclical scheduling routines. Mastering remainder problems builds foundational number theory competence for advanced mathematics. Option B results from an incorrect offset addition to the least common multiple baseline. Option C underestimates the required number by misapplying the decrease offset adjustment. Option D is far too small and fails to meet the basic least common multiple requirements.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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