Answer:
LCM = 840
Step-by-step explanation:
First, we need to find the prime factorization of every number. So 14, 21, and 40 are equal to the product of the following prime number:
14 = 2 x 7
21 = 3 x 7
40 = 2 x 2 x 2 x 5
Now, we need to identify all the prime numbers and the maximum number of times that every prime appears. So, the prime numbers are:
2 = Appears maximum 3 times
3 = Appears 1 time
5 = Appears 1 time
7 = Appears maximum 1 time
So, the LCM is the multiplication of the prime numbers as:
LCM = 2 x 2 x 2 x 3 x 5 x 7
LCM = 840
Therefore, the LCM is 840