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Example 8 Find the smallest square number which is divisible by each of the numbers 6, 9 and 15. Smallest square number divisible by 6, 9, 15 = L.C.M of 6, 9, 15 or Multiple of L.C.M Finding L.C.M 6, 9, 15 L.C.M of 6, 9, 15 = 2 × 3 × 3 × 5 = 90 Now, checking if 90 is a perfect square or not Checking if 90 is a perfect square 90 = 2 × 3 × 3 × 5 Since 2 & 5 do not occur in pairs Thus, we cannot calculate square root of 90 ∴ 90 is not a perfect square. So, we multiply by 2 and 5 to make pairs Thus, our number becomes 90 × 2 × 5 = 2 × 3 × 3 × 5 × 2 × 5 900 = 2 × 2 × 3 × 3 × 5 × 5 Now, it becomes a perfect square. Thus, required number is 900

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo