Question

The smallest square number which is exactly divisible by 2, 3, 9, 15 and 30 is _______ *
100
500
900
180​

Answer 1

Step-by-step explanation:

First find the LCM of 9,15 and 20 that is 180.

Now if you see the Prime factorization of 180, it is 2×2×3×3×5

So now to make 180 a perfect square we need to multiply it by 5 so that it's Prime factorization is 2×2×3×3×5×5.

Now 180×5=900

Now the square root of 900 is 30

Therefore, 30 is the smallest square number that is equally divisible by 9,15 and 20.

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Answer 2

Answer:

First find the LCM of 9,15 and 20 that is 180.

Now if you see the Prime factorization of 180, it is 2×2×3×3×5

So now to make 180 a perfect square we need to multiply it by 5 so that it's Prime factorization is 2×2×3×3×5×5.

Now 180×5=900

Now the square root of 900 is 30

Therefore, 30 is the smallest square number that is equally divisible by 9,15 and 20