Question

plzzzz solve class 10 maths 50 points........ The least number which is a perfect square and is divisible by each of 16, 20 and 24 is ​

Answer 1

Answer:

4 is the answer otherwise the answer is

Answer 2

It's too simple dear!

Let's first write prime factorization of 16 , 20 & 24

16 = 2*2*2*2 = 2^4

a perfect square

20 = 2*2*5 = (2^2)*5

24 = 2*2*2*3 = (2^3)*3

Now first obtain least number divisible by 16 , 20 and 24 which will be LCM of 16 , 20 & 24

So ,

LCM = highest power of each prime

= (2^4) * (3) * (5)

Now we get the LCM

But we have to find a number which is perfect square

Definitely LCM means lowest common multiple, which means any other common multiple of 16 , 20 & 24 will be multiple of LCM obtained above

So to make a perfect square definitely it should contain every prime number even times so it can be broken into two identical roots

LCM = (2^4) * (3) * (5)

To make it a perfect square :-

We multiply LCM with 3 & 5 so that every prime in LCM occurs even number of times

LCM * 3 * 5 = (2^4) * (3) * (5) * 3 * 5

= (2^4) * (3^2) * (5^2)

= [(2^2) * 3 * 5] * [ (2^2) * 3 * 5]

And this is your required answer

Answered by an IIT JEE ASPIRANT and all India mathematics OLYMPIAD TOPPER in class 10th