Question

Find the LCM of these two expressions:
m2 + 11m + 10 and m2 + 9m - 10.

Answer 1

The LCM of
`m^2 + 11m + 10\text{ and }m^2 + 9m - 10` is
`\bold{(m+1)(m-1)(m+10)}`

Solution:

On factorising
`m^2 + 11m + 10` we get,

`\Rightarrow m^2+m+10m+10\rightarrow m(m+1)+10(m+1)`

`\Rightarrow(m+1)(m+10)`

Therefore, the factors of m^2+11m+10 are (m+1)(m+10)

On factorising
`m^2 + 9m - 10` we get,

`\Rightarrow m^2-m+10m-10\rightarrow m(m-1)+10(m-1)`

`\Rightarrow(m-1)(m+10)`

Therefore, the factors of
`m^2+9m-10` are
`(m-1)(m+10)`

So, the LCM of both the given expressions will be
`(m+1)(m-1)(m+10)`

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.