1. Look at the two monomials below.
9u3v2w4 15u4v4w3
What is the least common multiple (LCM) of the monomials shown above?
3u3v2w3
45u4v4w4
45u3v2w3
3u4v4w4
First, i'm assuming there are no exponents. Then i'm going to multiply
the coefficients together forming a single coefficient for each monomial.
9u3v2w4 = 216uvw,
15u4v4w3 = 720uvw,
The LCM is => The largest coefficient(720). If we divided 720 by 216, we would get a remainder. Therefore, 720 is NOT the LCM. So the LCM is > 720.
We try dividing 2160(3*720) by 216 and
we get 10 and NO remainder.
Therefore, the LCM = 2160.
To find the least common multiple (LCM) of the given monomials, we need to find the highest power of each variable that appears in either monomial.
Let's break down the given monomials:
9u^3v^2w^4 15u^4v^4w^3
The variable 'u' appears with the highest power of 4 in the second monomial: 15u^4v^4w^3.
The variable 'v' appears with the highest power of 4 in the second monomial: 15u^4v^4w^3.
The variable 'w' appears with the highest power of 4 in the first monomial: 9u^3v^2w^4.
Now, multiply these highest powers together to find the LCM:
4 * 4 * 4 = 64
So, the LCM of the given monomials is 64u^4v^4w^4.
Therefore, the correct answer is:
45u^4v^4w^4.