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Prove that LCM {6!, 7!, 8!} = 8!

Answer»

To Prove : 

LCM {6!, 7!, 8!} = 8! 

Formula : n! = n x (n-1)!

LCM is the smallest possible number that is a multiple of two or more numbers. 

Here, we observe that (8!) is the first number which is a multiple of all three given numbers i.e. 6!, 7! and 8!.

1 x (8!) = 8!

8 x (7!) = 8!

8 x 7 x (6!) = 8!

Therefore, 8! is the LCM of {6!, 7!, 8!}

Conclusion : Hence proved


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