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# Find the smallest square number that is divisible by each of the numbers 8,15 and 20.

Q.10 Find the smallest square number that is divisible by each of the numbers $8,15$ and $20$.

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This has to be done in two steps. First we will find LCM of given numbers, then we will make it perfect square.

So the LCM of 8, 15, 20 is 120   .                                  8 = 2$\times$2$\times$2  ;           15 = 3$\times$5   ;             20 =  2$\times$2$\times$5

Prime factorisation of 120 gives = $2\times2\times2\times3\times5$ .

To make it a perfect square we need to multiply it with 30.

So the smallest square number that is divisible by each of the numbers 4, 9 and 10 is 3600.

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