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Easy: Identical kits: the GCF
Splitting things into the greatest number of identical groups uses the greatest common factor. Finding when two repeating events happen together again, or matching packs of different sizes, uses the least common multiple.
Decide whether each problem needs the GCF or the LCM, then solve it.
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If you are splitting things into equal groups with nothing left over, the answer can't be bigger than the numbers, so it is the GCF. If you are waiting for things to match up again, the answer is at least as big as the numbers, so it is the LCM.
Find the LCM of 10 and 8: multiples of 10 are 10, 20, 30, 40 and 40 is the first multiple of 8. So buy 40 hot dogs (4 packs) and 40 buns (5 packs).
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