Find the least common mutiple of 8c and 5c^2.
To find the least common multiple of 8c and 5c^2, we need to first factorize both expressions.
8c = 2^3 * c
5c^2 = 5 * c^2
Next, we need to determine the highest power of each prime factor that appears in either expression.
The prime factors in the factorization of 8c are 2 and c with powers 3 and 1 respectively. The prime factors in the factorization of 5c^2 are 5 and c with powers 1 and 2 respectively.
The least common multiple is the product of the highest powers of each distinct prime factor. Therefore, the least common multiple of 8c and 5c^2 is:
2^3 * 5 * c^2 = 40c^2