Prove that

Question:

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

 

Solution:

To Prove : LCM $\{6 !, 7 !, 8 !\}=8 !$

Formula: $n !=n \times(n-1) !$

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 $8 !$.

$1 \times(8 !)=8 !$

$8 \times(7 !)=8 !$

$8 \times 7 \times(6 !)=8 !$

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

Conclusion : Hence proved

 

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now