Question

15. Which is the smallest perfect square divisible by each of the numbers 8 , 16 , and 22 ? ​

Answer 1

Answer:

for 8 perfect square is 4

for 16 perfect square is 8

for 22 perfect square is 11

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Answer 2

Step-by-step explanation:

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

LCM = 23∗3∗5=12023∗3∗5=120

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

120 = 23∗3∗523∗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=360024∗32∗52=3600 .

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