1.FIND THE LCM OF
10X^7 AND 50X^4
2.FIND THE LCM OF
x^2 -36 AND x^2 + 11x +30
3.FIND THE LCM
y^3+8y^2+16y, y^2 -8y
4.FIND The LCM Of
15z^2 +60z and 3z^2 + 15z +12
10x^7 = 10x^4 * x^3
50x^4 = 10x^4 * 5
LCM = 10x^4 * 5x^3 = 50x^7
x^2 - 36 = (x+6)(x-6)
x^2 + 11x + 30 = (x+6)(x+5)
LCM = (x+6)(x-6)(x+5)
y^3 + 8y^2 + 16y = y(y+4)(y+4)
y^2 - 8y = y(y-8)
LCM = y(y+4)(y+4)(y-8)
15z^2 + 60z = 15z(z+4) = 3(z+4)*5z
3z^2 + 15z + 12 = 3(z+4)(z+1)
LCM = 15z(z+4)(z+1)
Find each of the following for x^2+5x+6 and x^2+x-2.
a) the LCM
b) the GCF
To find the least common multiple (LCM) of algebraic expressions, we need to follow these steps:
1. Factorize each expression completely.
2. Identify all the unique factors and their highest powers from both expressions.
3. Multiply all the unique factors with their highest powers obtained in step 2.
Now, let's apply this process to each problem:
1. Finding the LCM of 10x^7 and 50x^4:
Step 1: The expression 10x^7 can be factored into 2 * 5 * x * x * x * x * x * x * x.
The expression 50x^4 can be factored into 2 * 5 * 5 * x * x * x * x.
Step 2: The unique factors and their highest powers are 2 (power = 1), 5 (power = 2), and x (power = 4).
Step 3: Multiply the unique factors with their highest powers:
LCM = 2 * 5 * 5 * x * x * x * x * x * x * x
= 50x^4
Therefore, the LCM of 10x^7 and 50x^4 is 50x^4.
2. Finding the LCM of x^2 - 36 and x^2 + 11x + 30:
Step 1: The expression x^2 - 36 can be factored as (x - 6)*(x + 6).
The expression x^2 + 11x + 30 can be factored as (x + 5)*(x + 6).
Step 2: The unique factors and their highest powers are (x - 6) (power = 1), (x + 5) (power = 1), and (x + 6) (power = 1).
Step 3: Multiply the unique factors with their highest powers:
LCM = (x - 6) * (x + 5) * (x + 6)
Therefore, the LCM of x^2 - 36 and x^2 + 11x + 30 is (x - 6) * (x + 5) * (x + 6).
3. Finding the LCM of y^3 + 8y^2 + 16y and y^2 - 8y:
Step 1: The expression y^3 + 8y^2 + 16y can be factored as y * (y + 4) * (y + 4).
The expression y^2 - 8y can be factored as y * (y - 8).
Step 2: The unique factors and their highest powers are y (power = 1), (y + 4) (power = 2), and (y - 8) (power = 1).
Step 3: Multiply the unique factors with their highest powers:
LCM = y * (y + 4) * (y + 4) * (y - 8)
Therefore, the LCM of y^3 + 8y^2 + 16y and y^2 - 8y is y * (y + 4) * (y + 4) * (y - 8).
4. Finding the LCM of 15z^2 + 60z and 3z^2 + 15z + 12:
Step 1: The expression 15z^2 + 60z can be factored as 15z * (z + 4).
The expression 3z^2 + 15z + 12 can be factored as 3 * (z + 2) * (z + 2).
Step 2: The unique factors and their highest powers are 15z (power = 1), 3 (power = 1), and (z + 2) (power = 2).
Step 3: Multiply the unique factors with their highest powers:
LCM = 15z * 3 * (z + 2) * (z + 2)
Therefore, the LCM of 15z^2 + 60z and 3z^2 + 15z + 12 is 15z * 3 * (z + 2) * (z + 2).