Question

Compute: L.C.M. of $(6!,7!,8!)$

Answer 1

Hint: At first we define the term LCM, then using the definition of the L.C.M. we will find the LCM of the given number, in which we will first find the factors of the given number, and with the help of those factors we will determine the LCM to get the answer.

Complete step-by-step answer:
Given data: The numbers whose L.C.M. we will find $(6!,7!,8!)$
We know that L.C.M. refers to the lowest common multiple which means the lowest number such that it is the multiple of all those numbers whose LCM is to be found.
Writing the factors of the given numbers i.e. $(6!,7!,8!)$
$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1$
$7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$
$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$
From the above factors of the given numbers, we can say that 8! is the LCM of $(6!,7!,8!)$ as it is the lowest number which is the multiple of all the three numbers

Note: While finding the LCM of the number if we asked to find the LCM of prime numbers then their LCM is just the product of those prime numbers as they have factors other than 1 and itself.