Question
What is the least number which is a perfect square and divisible by 3, 10, 12, and 15?
Solution
LCM (3, 10, 12, 15) = 60 60 = 2 × 2 × 3 × 5 Here, 3 and 5 occur only once, and we already have 2 in a pair. To make all prime factors in pairs, multiply by another 3 and 5. ⇒ 60 × 3 × 5 = 900 ∴ 900 is the least perfect square divisible by 3, 10, 12, and 15.
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