Find the LCM
15b^3a^3, 5b^8,a^2, 6b^2a^6
LCM = 30a^6b^8
To find the LCM (Least Common Multiple) of these expressions, we need to find the highest power of each variable that appears in any of the expressions and multiply them together.
Let's break down each expression and find the highest power of each variable:
Expression 1: 15b^3a^3
The highest power of 'b' is b^3
The highest power of 'a' is a^3
Expression 2: 5b^8
The highest power of 'b' is b^8
The highest power of 'a' is a^0 (since a is not present)
Expression 3: a^2
The highest power of 'b' is b^0 (since b is not present)
The highest power of 'a' is a^2
Expression 4: 6b^2a^6
The highest power of 'b' is b^2
The highest power of 'a' is a^6
Now, we need to take the highest powers of each variable:
b: The highest power is b^8 (from Expression 2)
a: The highest power is a^6 (from Expression 4)
Multiplying the highest powers of each variable, we get:
b^8 * a^6 = b^(8+0) * a^6 = b^8 * a^6
Therefore, the LCM of 15b^3a^3, 5b^8, a^2, and 6b^2a^6 is 15b^8a^6.