Compute:(i) 30!/28!(ii) (11! – 10!)/9!(iii) L.C.M. (6!, 7!, 8!)

1.	Compute:(i) 30!/28!(ii) (11! – 10!)/9!(iii) L.C.M. (6!, 7!, 8!)
Answer» (i) 30!/28! Now, let us evaluate, 30!/28! = (30 × 29 × 28!)/28! = 30 × 29 = 870 (ii) (11! – 10!)/9! Now, let us evaluate, As we know that, 11! = 11 × 10 × 9 × …. × 1 10! = 10 × 9 × 8 × … × 1 9! = 9 × 8 × 7 × … × 1 On using these values we get, (11! – 10!)/9! = (11 × 10 × 9! – 10 × 9!)/9! = 9!(110 – 10)/9! = 110 – 10 = 100 (iii) L.C.M. (6!, 7!, 8!) Now, let us find the LCM of (6!, 7!, 8!) As we know that, 8! = 8 × 7 × 6! 7! = 7 × 6! 6! = 6! Therefore, L.C.M. (6!, 7!, 8!) = LCM [8 × 7 × 6!, 7 × 6!, 6!] = 8 × 7 × 6! = 8!

Answer»

(i) 30!/28!

Now, let us evaluate,

30!/28! = (30 × 29 × 28!)/28!

= 30 × 29

= 870

(ii) (11! – 10!)/9!

Now, let us evaluate,

As we know that,

11! = 11 × 10 × 9 × …. × 1

10! = 10 × 9 × 8 × … × 1

9! = 9 × 8 × 7 × … × 1

On using these values we get,

(11! – 10!)/9! = (11 × 10 × 9! – 10 × 9!)/9!

= 9!(110 – 10)/9!

= 110 – 10

= 100

(iii) L.C.M. (6!, 7!, 8!)

Now, let us find the LCM of (6!, 7!, 8!)

As we know that,

8! = 8 × 7 × 6!

7! = 7 × 6!

6! = 6!

Therefore,

L.C.M. (6!, 7!, 8!) = LCM [8 × 7 × 6!, 7 × 6!, 6!]

= 8 × 7 × 6!

= 8!

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