Both start with finding the prime factorizations of the given numbers. The difference is which of those factors you select.
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Whenever one number is a multiple of the other, the LCM is the larger number and the GCF is the smaller number. The difference is 42.
The GCF of 18, 20, and 26 is 2. The GCF of a set of numbers can't be any larger than the smallest difference between the numbers. The smallest difference within this set of numbers is 2. Since all of the numbers in the set are even, 2 is the greatest common factor.
Math is all about getting the most precise answer. You could reduce the fraction 8/12 to 4/6 but if you know that the GCF of 8 and 12 is 4, you can take 4 out of both of those and get 2/3, the simplest form. This makes a larger difference as numbers get larger.
605 - 11 = 594
16, 32 and 48 have a GCF of 16. Whether you added or multiplied to get them doesn't make much difference.