Find the LCM of 8x^2y^3 and 20xy^5.
Let me see.
I say 8 = 4 • 2. I can then say 4 = 2 • 2.
From this, I get 2 • 2 • 2. In prime factorization form, I get 2^3.
Now 20 = 4 • 5. Again, 4 = 2 • 2.
From this, I get 2 • 2 • 5. In prime factorization form, I get 2^2 • 5.
From a list containing 2^2 and 2^3, I take the number with the greatest exponent as part of my answer. I must include 5 in my answer because it is the only 5 available.
The first polynomial has x^2. The second term has x. I take the term with the greatest exponent as part of my answer. I take x^2.
The first polynomial also has y^3. The second polynomial has y^5. I take the polynomial with the greatest exponent which is y^5.
My LCM = 2^3 • 5 x^2y^5 or 40x^2y^5.
You say?
Let me see.
I say 8 = 4 • 2. I can then say 4 = 2 • 2.
From this, I get 2 • 2 • 2. In prime factorization form, I get 2^3.
Now 20 = 4 • 5. Again, 4 = 2 • 2.
From this, I get 2 • 2 • 5. In prime factorization form, I get 2^2 • 5.
From a list containing 2^2 and 2^3, I take the number with the greatest exponent as part of my answer. I must include 5 in my answer because it is the only 5 available.
The first polynomial has x^2. The second term has x. I take the term with the greatest exponent as part of my answer. I take x^2.
The first polynomial also has y^3. The second polynomial has y^5. I take the polynomial with the greatest exponent which is y^5.
My LCM = 2^3 • 5 x^2y^5 or 40x^2y^5.
You say?