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

Answers (1)

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

So the LCM of 4, 9, 10 is   180.                                  4 = 2\times2  ;           9 = 3\times3   ;             10 =  2\times5

Prime factorisation of 180 gives = 2\times2\times3\times3\times5.

To make it a perfect square we need to multiply it with 5.

So, the smallest square number which is divisible by each of the numbers 4, 9 and 10 = 900.

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