G
Guest
Guest
How do you get the LCM out of prime factorization? Please help?
B-RiZzY said:
The LCM is the product of the greatest number of prime factors of two or more numbers.
For example: if you had two fractions, 3/6 and 3/8, you would find the LCM for the common denominator this way:
factors of 6: 2 * 3
factors of 8: 2 * 2 * 2
the greatest number of 2s is 2*2*2
the greatest number of 3s is 3
LCM = 2*2*2*3 = 24.
If the fractions had been 5/18 and 3/8, then:
factors of 18: 2*3*3
factors of 8: 2*2*2
greatest number of 2s is three 2*2*2
greatest number of 3s is two 3*3
LCM = 2*2*2*3*3 = 72
If these two examples aren't sufficient to help you, post an actual problem that you'd get help on and show your work.
pka
Elite Member
- Joined
- Jan 29, 2005
- Messages
- 11,976
Factor each number into its prime factorization.
Then list each prime factor that appears in either number.
Select for each prime factor the greatest power that appears in either number.
That will give you the LCM.
Example:
If we have \(\displaystyle \L
N = 2^3 \cdot 3^2 \cdot 5^4 \cdot 11\) and \(\displaystyle \L
M = 2 \cdot 3^4 \cdot 5^2 \cdot 7^2\),
then the \(\displaystyle \L
LCM(N,M) = 2^3 \cdot 3^4 \cdot 5^4 \cdot 7^2 \cdot 11\)
Then list each prime factor that appears in either number.
Select for each prime factor the greatest power that appears in either number.
That will give you the LCM.
Example:
If we have \(\displaystyle \L
N = 2^3 \cdot 3^2 \cdot 5^4 \cdot 11\) and \(\displaystyle \L
M = 2 \cdot 3^4 \cdot 5^2 \cdot 7^2\),
then the \(\displaystyle \L
LCM(N,M) = 2^3 \cdot 3^4 \cdot 5^4 \cdot 7^2 \cdot 11\)
G
Guest
Guest
thanks people, it helped me a lot, respect to you two.