Question

Find the smallest square number which is divisible by each of the following number6,9,15

Answer 1

First we will find the LCM of the numbers

2 | 6,9,15
3 | 3,9,15
3 | 1,3,5
5 | 1,1,5
   | 1,1,1

Now we have to multiply these factors=2*3*3*5
                                                            =90
Now as this is not a perfect square we will do prime factorization.
2 | 90
3 | 45
3 | 15
5 | 5
   | 1

Now to get a perfect square we will need pairs of factors.If pairs are not there we will multiply the factors remaining i.e. there is one 2 and one 5 less so we will multiply these and then multiply the product to the LCM to get a perfect square.

2*5=10
90*20=900
 
Therefore the perfect square we want is 900.