Question

Find the l.c. m. of 4!,5!,6!.

Answer 1

4!=4×3×2×1
5!=5×4×3×2×1
6!=6×5×4×3×2×1
So LCM of the above numbers is 6!=720

Answer 2

Given:

We have given factorial of some numbers 4,5,and 6.

To Find:

We have to find the L.C.M of the above numbers?

Step-by-step explanation:

• We have given numbers  with factorial form 4!, 5! ,6!
• We can write them as the open form of factorial by comparing them with n! And we can open the form of factorial.

       $n!=n(n-1)\cdots2.1$

• Hence another factorial can also be opened by using the above formula by comparing the number with n.

       $4!=4\times3\times2\times1=24\\5!=5\times4\times3\times2\times1=120\\6!=6\times5\times4\times3\times2\times1=720$

• Now we also have the factors of 24, 120, and 720 from which we can write it the L.C.M is 720.

• Or we can find it by directly using the property which says that L.C.M of the consecutive factorial term is the largest factorial value you just need to simplify the form of factorial.

Hence, the L.C.M is 720.