10x^(6), 50x^(4)
what is the LCM
10=2*5
50=2*5^2
LCM(10,50) = 2*5^2 = 50
So, your LCM is 50x^6
Highest powers of all prime factors, considering x a "prime"
To find the least common multiple (LCM) of 10x^6 and 50x^4, we need to express both terms in their prime factorized form.
Let's start with 10x^6:
10 can be factored as 2 * 5.
x^6 can be written as (x^2)^3.
So, 10x^6 can be expressed as (2 * 5) * (x^2)^3 = 2^1 * 5^1 * x^2^3.
Now, let's factorize 50x^4:
50 can be factored as 2 * 5 * 5.
x^4 can be written as (x^2)^2.
So, 50x^4 can be expressed as (2 * 5 * 5) * (x^2)^2 = 2^1 * 5^2 * x^2^2.
Now, find the highest power of each prime factor that appears in either 10x^6 or 50x^4 and multiply them together to get the LCM:
2: The highest power is 1 in 10x^6 and 1 in 50x^4. So, take 2^1.
5: The highest power is 1 in 10x^6 and 2 in 50x^4. So, take 5^2.
x: The highest power is 2 in 10x^6 and 2 in 50x^4. So, take x^2.
Now, multiply these values together to get the LCM:
LCM = 2^1 * 5^2 * x^2 = 10x^2.