find the LCM of 15ef and 12e^4 (12e to the power of 4) Please show the steps. I do not understand how to do this.
Check for typos please
(12e) to the power of 4 is not 12 e^4.
It is 20,736 e^4
12 e^4 = 4*e^3 * 3e
15 ef = 5f*3e
They have a common factor 3e
LCM (lowest common multiple)
= 3e*5f*4e^3
= 60 e^4 f
Simplify 12e − 5f − 7e +3f.
Simplify 12e − 5f − 7e +3f.(1 point)
To find the least common multiple (LCM) of two expressions, we need to first factorize each expression and then determine the highest power of each factor present in either of the expressions.
Let's factorize each expression separately:
Expression 1: 15ef
- We can see that 15 is divisible by 3 and 5.
- The variable e does not have any factors.
- The variable f does not have any factors.
Therefore, 15ef does not have any further factorization.
Expression 2: 12e^4
The number 12 can be factored into 2 and 6, and 6 can be further factored into 2 and 3.
- We have the factor 2 occurring twice.
- The variable e has a power of 4.
- The variable f does not have any factors.
Now that we have factorized both expressions, we identify the factors and their highest powers in either expression:
- Factor 2: The highest power of 2 present is 2 (from expression 2).
- Factor 3: The highest power of 3 present is 1 (from expression 2).
- Factor 5: The highest power of 5 present is 1 (from expression 1).
- Variables e and f both have a power of 1 (from expressions 1 and 2).
Finally, we multiply all the factors together, considering their highest powers:
LCM = 2^2 * 3^1 * 5^1 * e^1 * f^1
= 4 * 3 * 5 * e * f
= 60ef
Therefore, the LCM of 15ef and 12e^4 is 60ef.