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The factor tree finds the prime factorizations The prime factorizations find the GCF and LCM.
Example 30 and 42:
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 common factors.
2 x 3 = 6, the GCF
Combine the factors, eliminating duplicates.
2 x 3 x 5 x 7 = 210, the LCM
Check it.
30 x 42 = 1260
210 x 6 = 1260
It checks.


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Q: How can you find the LCM and HCF by using the factor tree?
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