How to find lcm using prime factoriazation
http://www.mathsisfun.com/least-common-multiple.html
http://www.mathsisfun.com/prime-factorization.html
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Finding the least common multiple (LCM) using prime factorization involves breaking down each number into its prime factors and then finding the product of the highest powers of all the prime factors.
To find the LCM using prime factorization, follow these steps:
1. Start by prime factorizing each number separately.
- Take the first number and identify its prime factors.
- Repeat the process for the second number.
- Ensure that you include all prime factors and their respective powers.
2. Identify the common prime factors from both sets of prime factorizations.
- Take note of the common prime factors and their corresponding highest power.
3. Multiply the common prime factors with their respective highest powers.
- Multiply all the common prime factors with their corresponding highest powers to get the LCM.
Let's take an example to understand the process:
Example: Find the LCM of 12 and 18 using prime factorization.
Step 1: Prime factorize each number.
- 12 = 2^2 * 3
- 18 = 2 * 3^2
Step 2: Identify the common prime factors.
- The common prime factors between 12 and 18 are 2 and 3.
Step 3: Multiply the common prime factors with their highest powers.
- For the prime factor 2, the highest power is 2.
- For the prime factor 3, the highest power is 2.
The LCM of 12 and 18 is (2^2) * (3^2) = 4 * 9 = 36.
Therefore, the LCM of 12 and 18 using prime factorization is 36.