+11912 Find the smallest square number that is divisible by each of the numbers 4, 9 and 10 ?
So can anyone explain this question to me nicely in a very easy way?
+128661 Notice, rosala that if the number is divisible by 10, the square itself must end with a "0." And the only way that's possible is if the number we are squaring itself ends with a zero.
Let's factor each number:
4 = 2^2
9 = 3^2
10 = 5 * 2
And notice, if I select all the different factors, I get 2, 3 and 5. And multiplying them together, we get 2*3*5 = 30.
Now square this number ....30^2 = 900
And that's the smallest square that is divisible by 4, 9 and 10 !!!!
Why does this work?? .....Note that 900 = 25*36 = 25*9*4........so 4 and 9 will divide this, and since it ends in a "0," so will 10....!!!!!
Hope that helps!!
+128661 Notice, rosala that if the number is divisible by 10, the square itself must end with a "0." And the only way that's possible is if the number we are squaring itself ends with a zero.
Let's factor each number:
4 = 2^2
9 = 3^2
10 = 5 * 2
And notice, if I select all the different factors, I get 2, 3 and 5. And multiplying them together, we get 2*3*5 = 30.
Now square this number ....30^2 = 900
And that's the smallest square that is divisible by 4, 9 and 10 !!!!
Why does this work?? .....Note that 900 = 25*36 = 25*9*4........so 4 and 9 will divide this, and since it ends in a "0," so will 10....!!!!!
Hope that helps!!
