Question

find the smallest sqaure number which is divisible by 8,12 and 15

Answer 1

8=238=23

12=22∗312=22∗3

15=3∗515=3∗5

20=22∗520=22∗5

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.

So, required answer is 3600.

Answer 2

Step-by-step explanation:

3600 is your answer

hope it's helpful.