Question

Find the least square number which is exactly divisible by each of the numbers 8,12,15,20​

Answer 1

Step-by-step explanation:

What is the least perfect square number which is divisible by each of numbers 8, 12, 15, and 20?

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The answers given are all correct.

8=23

12=22∗3

15=3∗5

20=22∗5

So choosing the maximum of all the prime exponents that exist in the numbers above, we have,

LCM = 23∗3∗5=120

Now, I will use an approach which others have not used to get to the least perfect square.

120 = 23∗3∗5

Now in a perfect square, ALWAYS, exponent of each prime is always even.

So, we will change the exponent of 2 from 3 to 4.

We will change the exponent of 3 from 1 to 2.

We will change the exponent of 5 from 1 to 2.

Finally we have the number 24∗32∗52=3600 .

So, required answer is 3600.

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