Lcm of 8b^2 and 10c^4

To find the least common multiple (LCM) of 8b^2 and 10c^4, we need to factor both expressions completely.

Factor 8b^2:
8 = 2^3
b^2 = b^2

Factor 10c^4:
10 = 2 * 5
c^4 = c^4

Now, we need to find the LCM by taking the highest power of each prime factor that appears in either expression:
LCM = 2^3 * 5 * b^2 * c^4
LCM = 8 * 5 * b^2 * c^4
LCM = 40b^2c^4

Therefore, the LCM of 8b^2 and 10c^4 is 40b^2c^4.