Answer:
<em>LCM of both polynomials=</em>![\mathbf{5m^3}](https://tex.z-dn.net/?f=%5Cmathbf%7B5m%5E3%7D)
Step-by-step explanation:
<u>Least Common Multiple</u>
We are given the polynomials
![5m^7+ 35m^6+50m^5](https://tex.z-dn.net/?f=5m%5E7%2B%2035m%5E6%2B50m%5E5)
![-20m^5-80m^4+100m^3](https://tex.z-dn.net/?f=-20m%5E5-80m%5E4%2B100m%5E3)
Find the common factors of each polynomial, first the coefficients:
5 = 5
35 = 5*7
50 = 5*5*2
The common factor with the least exponent; 5
Now for the variables:
![m^7, m^6, m^5](https://tex.z-dn.net/?f=m%5E7%2C%20m%5E6%2C%20m%5E5)
The common factor with the least exponent; m^5
LCM of ![5m^7+ 35m^6+50m^5: 5m^5](https://tex.z-dn.net/?f=5m%5E7%2B%2035m%5E6%2B50m%5E5%3A%205m%5E5)
Similarly:
20 = 2*2*5
80=2*2*2*2*5
100 = 2*2*5*5
Common factor of the coefficients: 2*2*5=20
Common factor of variables: ![m^3](https://tex.z-dn.net/?f=m%5E3)
LCM of ![-20m^5-80m^4+100m^3 = 20m^3](https://tex.z-dn.net/?f=-20m%5E5-80m%5E4%2B100m%5E3%20%3D%2020m%5E3)
LCM of both polynomials=![\mathbf{5m^3}](https://tex.z-dn.net/?f=%5Cmathbf%7B5m%5E3%7D)