15 12 × _____ = perfect square

1.	15 12 × _____ = perfect square
Answer» 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. thanks mark me as brainliest :-)

Answer»

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.

thanks

mark me as brainliest :-)

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