What is the smallest square number divisible by 8, 12, and 18________?
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Answer: D. 144
Explanation
Finding the least common multiple of eight, twelve, and eighteen yields a base value of seventy-two. Prime factorization of seventy-two reveals factors that lack complete squared pairings for all primes. Multiplying seventy-two by two gives one forty-four, which is the smallest square number divisible by all factors. A square number must have even exponents for all prime factors in its prime factorization breakdown. Least common multiple represents the lowest building block number divisible by each given divisor. Multiplying an LCM by missing prime factors ensures the resulting product forms a complete square.
Number theory problems often require constructing minimum square numbers for grid and tile arrangements. Architects use square number properties when designing symmetrical floor tile and paving patterns. Understanding prime factorization structures helps students solve advanced divisibility questions quickly. Option A is a square number but fails the divisibility test for all the given factors. Option B is an odd square number that is not divisible by even factors like eight and twelve. Option C is a square number but is smaller than the least common multiple required by the divisors.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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