Find LCM of Polynomials...3

[feliz_nyc]

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?

 

[Dr.Peterson]

Find the LCM of 8x^2y^3 and 20xy^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?

Looks like you've learned one of the orderly methods. Good.

To state what you've done more visibly, you have

8x^2y^3 = 2^3 5^0x^2 y^3​

20xy^5 = 2^2 5^1 x^1 y^5​

so the LCM has the same factors, with the largest exponent on each,

2^3 5^1 x^2 y^5 = 40x^2y^5.​

Good work, and well explained.

 

[feliz_nyc]

Looks like you've learned one of the orderly methods. Good.

To state what you've done more visibly, you have

8x^2y^3 = 2^3 5^0x^2 y^3​

20xy^5 = 2^2 5^1 x^1 y^5​

so the LCM has the same factors, with the largest exponent on each,

2^3 5^1 x^2 y^5 = 40x^2y^5.​

Good work, and well explained.

I worked on this for at least 12 minutes.