Consider the following statements. I. The continued product of first n natural numbers is called the permutation. II. L.C.M of 4 !, 5 ! and 6 ! is 720 . Choose the correct option.

Question

Consider the following statements. I. The continued product of first n natural numbers is called the permutation. II. L.C.M of 4 !, 5 ! and 6 ! is 720 . Choose the correct option. (A) Only I is true. (B) Only II is true. (C) Both are true. (D) Both are false.

Tardigrade Admin · Accepted Answer

I. The continued product of first n natural numbers is called the 'n factorial'.
II.

5! = 5 \times 4!

6! = 6 \times 5 \times 4!

∴

L.C.M. of

4!, 5!, 6!

=

L.C.M.

[4!, 5 \times 4!, 6 \times 5 \times 4!]

= 4! \times 5 \times 6 = 6! = 720

Q. Consider the following statements. I. The continued product of first n natural numbers is called the permutation. II. L.C.M of 4!,5! and 6! is 720 . Choose the correct option.

Only I is true.

Only II is true.

Both are true.

Both are false.

I. The continued product of first n natural numbers is called the 'n factorial'. II. 5!=5×4! 6!=6×5×4! ∴ L.C.M. of 4!,5!,6! = L.C.M. [4!,5×4!,6×5×4!] =4!×5×6=6!=720

Q. Consider the following statements.
I. The continued product of first $n$ natural numbers is called the permutation.
II. L.C.M of $4!, 5!$ and $6!$ is $720$ .
Choose the correct option.

I. The continued product of first n natural numbers is called the 'n factorial'.
II. $5! = 5 \times 4!$
$6! = 6 \times 5 \times 4!$
$∴$ L.C.M. of $4!, 5!, 6!$
$=$ L.C.M. $[4!, 5 \times 4!, 6 \times 5 \times 4!]$
$= 4! \times 5 \times 6 = 6! = 720$