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Two different problems: A factor tree is a way to notate the process of finding the prime factorization of a given number. Once you have the prime factorizations of at least two numbers, you can combine them and find the LCM.

All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210.

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the highest amount of each factor.

2 x 3 x 5 x 7 = 210, the LCM

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The LCM of a set of integers is the smallest positive integer which can be divided evenly by each number in the set. The LCM of the set is the same however it is calculated.

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Q: What is the LCM using the factor tree?
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What is the LCM with prime factorization using a factor tree using numbers 3 and 4?

That's a lot of extra work for this problem but here goes. 3 is already prime so it doesn't really have a factor tree or prime factorization. The prime factorization of 4 is 2 x 2 which looks like this in a factor tree.42,23 and 4 have no common prime factors, so the LCM is their product, 12


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The factor tree finds the prime factorization. The prime factorization finds the LCM. Example: 30 and 42 Factor them. 30 15,2 5,3,2 42 21,2 7,3,2 2 x 3 x 5 = 30 2 x 3 x 7 = 42 Select the highest amount of each factor. 2 x 3 x 5 x 7 = 210, the LCM


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