Find the smallest square number which is divisible by each of the numbers 6, 9 and 15 ?

We will first find out the L.C.M of 6, 9 and 15.

L.C.M of 6, 9, 15 = 2 × 3 × 3 × 5 = 2 × 3^{2 } × 5 = 90

Since, we need to find the smallest square number divisible by 6, 9 and 15 and in above prime factorization of the numbers we observe that 2 and 5 does not appear in pair, therefore we multiply the L.C.M, 90 by 2 × 5.

Hence,

The required smallest square number = 90 × 2 × 5 = 900.

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