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Use Prime Factorization to Find LCM. From my previous lesson, I went over the steps on how to find the LCM of two positive integers using the List Method. This time I will focus on the method where Prime Factorization is used to find the LCM.
Find the prime factorization of a composite number; Find the least common multiple (LCM) of two numbers
HOW TO: FIND THE LCM USING THE PRIME FACTORS METHOD. Step 1. Find the prime factorization of each number. Step 2. Write each number as a product of primes, matching primes vertically when possible. Step 3. Bring down the primes in each column. Step 4. Multiply the factors to get the LCM.
We can use prime factorization to find the smallest common multiple of two positive integers. The least common multiple (l.c.m.) of two positive integers is the smallest positive integer that is a multiple of both.
Example 1. Determine the prime factorization of 340. There are many ways to solve this problem. One approach is to create a prime factorization tree. Since 340 is even we can remove a factor of 2. 170 remains. Then we can remove 17 from 170 and so on. 340 170. 17 10. ∴ the prime factorization of 340 is 340 = 2 · 2 · 5 · 17 = 22 · 5 · 17.
Composite numbers have more than two factors, and every composite number can be written as a unique product of primes. This is called the prime factorization of a number. When we write the prime factorization of a number, we are rewriting the number as a product of primes.
The factor [latex]4[/latex] is composite, and it factors into [latex]2\cdot 2[/latex]. We write these factors under the [latex]4[/latex]. Since [latex]2[/latex] is prime, we circle both [latex]2\text{s}[/latex]. The prime factorization is the product of the circled primes. We generally write the prime factorization in order from least to greatest.
