Answer: The smallest value of n is:
n = 21
Explanation:
We know that the LCM (least common multiple) between 120 and n is 2520.
We want to find the smallest value of n.
The smallest value of n will be such that n does not share any prime number with 120, then the greatest common factor between 120 and n is 1.
Remember that the LCM between A and B is:
LCM(A, B) = A*B/(GCM(A, B))
Then if the greatest common factor between A and B is 1, we will have:
LCM(A, B) = A*B
Then if the greatest common factor between 120 and n is 1, we have that:
LCM(120, n) = 120*n = 2520
then:
n = 2520/120 = 21
The smallest value of n is n = 21.