Question

find the smallest perfect square number that is divisible by 6 ,7 ,8 and 27​

Answer 1

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Answer 2

Question :- find the smallest perfect square number that is divisible by 6 ,7 ,8 and 27 ?

Solution :-

As , we know that, to find the smallest number divisible by given numbers first we have to find the LCM.

So, Lets first find the LCM of given numbers .

Prime Factors of 6, 7, 8 and 27 :-

→ 6 = 2 * 3

→ 7 = 1 * 7

→ 8 = 2 * 2 * 2

→ 27 = 3 * 3 * 3

LCM = 2³ * 3³ * 7

Now, we need a perfect Square number . As we know that, Perfect square we have pair of two of each prime factors .

→ LCM = (2 * 2) * 2 * (3 * 3) * 3 * 7

In order to make LCM a perfect square we need to multiply the LCM by 2 , 3 and 7 .

Therefore,

→ Required Number = LCM * 2 * 3 * 7

→ Required Number = 2³ * 3³ * 7 * 42

→ Required Number = 8 * 27 * 294

→ Required Number = 63,504. (Ans.)

Hence, the Least perfect square number is 63,504.

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