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What is the smallest perfect square that is divisible by 10, 12, 15, and 18?

Problems on L.C.M and H.C.F MCQs for PPSC, FPSC, NTS, and Pakistan government job tests. Select an option below, then read the explanation.

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Problems on L.C.M and H.C.Fmathematics-mcqs › problems-on-l-c-m-and-h-c-f
Published
12 Jul 2019
Last updated
28 May 2026

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Explanation

To find the smallest perfect square divisible by 10, 12, 15, and 18, first determine their least common multiple (LCM). The LCM is 180. The prime factorization of 180 is 2² × 3² × 5. To make it a perfect square, all prime exponents must be even. Since 5 has an exponent of 1, multiply by another 5 to get 900 (which is 30²). Thus, 900 is the smallest perfect square divisible by all given numbers.

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