What is the least perfect square which is divisible by 24 30 and 60?

2 answers:

6 0

Step 1: LCM of 24 , 30 and 60 = 120

so 120 is the least no which is divisible by all 24 , 30 and 60

Step 2: factors of 120 will be 2^3 * 3 * 5

so the least perfect square, which is divisible by 24, 30 and 60 will be
(2^3 * 3 * 5) x ( 2 * 3 * 5 ) = 3600

3600

exis [7]2 years ago

5 0

Answer: 3600 is the least perfect square number which is divisible by 24,30 and 60.

Step-by-step explanation:

Since we have given that

The numbers are 24,30 and 60.

We need to find the least perfect square.

First we find the L.C.M. of 24, 30 and 60 .

So, L.C.M. of 24, 30 and 60 = 120

But 120 is not a perfect square because:

120=2×2×2×3×5

Since 2,3 and 5 has no pair.

We will multiply with 2,3,and 5.

So, it becomes,

2×2×2×3×5×2×3×5

=3600

Hence, 3600 is the least perfect square number which is divisible by 24,30 and 60.

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Let G denote the centroid of triangle ABC. If triangle ABG is equilateral with side length 2, then determine the perimeter of tr

zhannawk [14.2K]

We know from Euclidean Geometry and the properties of a centroid that GC=2GM. Now GM=sin60*GA= $\sqrt{3}$ . Hence CM=GC+GM=3* $\sqrt{3} /$ . Now, since GM is normal to AB, we have by the pythagoeran theorem that:
$AC^2=AM^2+GM^2=BM^2+GM^2=BC^2$
Hence, we calculate from this that AC^2= 28, hence AC=2* $\sqrt{7}$ =BC. Thus, the perimeter of the triangle is 2+4* $\sqrt{7}$ .