The LCM of [tex]m^2 + 11m + 10\text{ and }m^2 + 9m - 10[/tex] is [tex]\bold{(m+1)(m-1)(m+10)}[/tex]
Solution:
On factorising [tex]m^2 + 11m + 10[/tex] we get,
[tex]\Rightarrow m^2+m+10m+10\rightarrow m(m+1)+10(m+1)[/tex]
[tex]\Rightarrow(m+1)(m+10)[/tex]
Therefore, the factors of m^2+11m+10 are (m+1)(m+10)
On factorising [tex]m^2 + 9m - 10[/tex] we get,
[tex]\Rightarrow m^2-m+10m-10\rightarrow m(m-1)+10(m-1)[/tex]
[tex]\Rightarrow(m-1)(m+10)[/tex]
Therefore, the factors of [tex]m^2+9m-10[/tex] are [tex](m-1)(m+10)[/tex]
So, the LCM of both the given expressions will be [tex](m+1)(m-1)(m+10)[/tex]
Steps to find the LCM (Least Common Multiple) of two given monomials or polynomials:
Step 1: Find all the factors of all the expressions being multiplied.
Step 2: Multiply together one of each unique factor, and the repeat factors with the highest exponents.
