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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To find the GCF and the LCM you have to first at least try to use prime factorization. So use factor trees. Or for the LCM find th least common multiples of the number.
The LCM of 100 and 60 is 300.You can find that is by doing the simplest thing like upside down division of a factor tree. You have to divide with a prime number such as 2,3,5,7,11,13 or a number that cannot be divided by anything but 1 and itself.
The HCF is always a factor of the LCM of two numbers. The HCF is a factor of both the numbers which are factors of their LCM. Thus the HCF is also a factor of the LCM of the two numbers.
66 33,2 11,3,2
2x2x222