What is the LCM of 15x^6 and 75x^8?
maybe 75 x^8 because
15 x^6 * 5 x*2 = 75 x^8 * 1
LCM of 15x^3 and 45^4
To find the least common multiple (LCM) of the given expressions, we need to break down both expressions into their prime factorizations.
Let's start with 15x^6:
The prime factorization of 15 can be written as 3 * 5.
The prime factorization of x^6 can be written as x * x * x * x * x * x.
Now, let's look at 75x^8:
The prime factorization of 75 can be written as 3 * 5 * 5.
The prime factorization of x^8 can be written as x * x * x * x * x * x * x * x.
Now, we need to find the highest power of each prime factor that appears in either expression.
For the prime factor 3, it appears once in 15x^6 and once in 75x^8. So, we take the higher power, which is 1.
For the prime factor 5, it appears once in 15x^6 and twice in 75x^8. So, we take the higher power, which is 2.
For the variable x, it appears 6 times in 15x^6 and 8 times in 75x^8. So, we take the higher power, which is 8.
Now, we can put everything together: LCM = 3 * 5^2 * x^8 = 75x^8.
Therefore, the LCM of 15x^6 and 75x^8 is 75x^8.