Question

find the smallest square that is divided by each of number 8,15 and 20

Answer 1

Hiiii,
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The smallest number is 120  . 
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Answer 2

Hey There!!!

To solve this problem, let us first analyze what data we have. We will factorise all these numbers:

$8=2^3 \\ \\ 15=3\times 5 \\ \\ 20=2^2\times 5$

We can see that LCM will be:

$LCM=2^3\times 3 \times 5 = 120$

The LCM of 8, 15 and 20 is 120. All numbers divisible by the LCM are also divisible by 8, 15 and 120

Now, we want the smallest perfect square which is divisible by 120. Here again we look at the prime factorization of 120. 

We have:$120=2^3\times 3\times 5$

We see that if we can get $2^4,\, 3^2, \, and \, 5^2$, we can make a perfect square.


So, for that we need to multilply 120 by 2, 3 and 5.

So, smallest perfect square which is a multiple of 120 is:

$Ans=120\times 2 \times 3 \times 5 \\ \\ \boxed{Ans=3600=60^2}$


Thus, 3600 is the smallest square which is divisible by each of 8, 15 and 20.


Hope it helps
Purva
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