15z^2+45z and 5z^2+40z+75 find Lcm
15z^2+45z
=15z(z+3)
5z^2+40z+75
= 5(z^2 + 8z +15)
= 5(z+5)(z+3)
LCM = 15z(z+3)(z+5)
To find the least common multiple (LCM) of the given polynomials 15z^2 + 45z and 5z^2 + 40z + 75, we need to factor each polynomial completely.
Let's start with the first polynomial, 15z^2 + 45z. We can factor out a common factor of 15z from each term:
15z^2 + 45z = 15z(z + 3)
Now let's factor the second polynomial, 5z^2 + 40z + 75. We can start by looking for common factors among the coefficients of the terms. In this case, there is a common factor of 5:
5z^2 + 40z + 75 = 5(z^2 + 8z + 15)
Next, we need to factor the quadratic expression inside the parentheses. We are looking for two numbers that multiply to give 15 and add up to give 8. The numbers we are looking for are 3 and 5:
z^2 + 8z + 15 = (z + 3)(z + 5)
Now we have completely factored both polynomials:
15z^2 + 45z = 15z(z + 3)
5z^2 + 40z + 75 = 5(z + 3)(z + 5)
To find the LCM, we need to take the product of the highest powers of all the common factors. In this case, the common factor is (z + 3). So the LCM is:
15z(z + 3)(z + 5)
Thus, the LCM of 15z^2 + 45z and 5z^2 + 40z + 75 is 15z(z + 3)(z + 5).