Question

*Find the least perfect square which is divisible by 10,12 and 8​​

Answer 1

The LCM of numbers 8, 10 and 12 is 120.

Going deeper into the LCM process, factorizing 8, 10 and 12, we get

8=2∗2∗28=2∗2∗2

10=2∗510=2∗5

12=2∗2∗312=2∗2∗3

So the LCM of these numbers would be 2∗2∗2∗3∗5=1202∗2∗2∗3∗5=120

Now, the square of any number would be a product of an even number of numbers. And here we have 2 repeated thrice, 3 and 5 repeated once each. So we need 2 repeated 4 times, 3 and 5 repeated twice each (to get the higher even number than we already have).

Therefore, we get 2∗2∗2∗2∗3∗3∗5∗5=36002∗2∗2∗2∗3∗3∗5∗5=3600

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