GCF or LCM?

Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 16 of 58.

Word problems rarely say 'GCF' or 'LCM', so you decide which one the story needs. Ask what is happening. If two amounts are being split into equal groups with nothing left over, the group count divides both amounts: that is a common factor, and the biggest such count is the GCF.

If things repeat or come in packs and you want them to line up, the answer is a number both go into: a common multiple, and the smallest is the LCM. Cups come in stacks of 6 and lids in stacks of 9. To have exactly as many cups as lids, the count must be a multiple of 6 and of 9, and the smallest is 18: 3 stacks of cups and 2 stacks of lids.

A quick check on your choice: a GCF answer is never bigger than the numbers in the story, and an LCM answer is never smaller. If your result goes the wrong way, you picked the wrong one.

Challenge

Hot dogs come in packs of 10 and buns come in packs of 8. You buy whole packs of each and want exactly as many hot dogs as buns. Find the smallest number L of hot dogs (and of buns) you can end up with. Write L = ... on the board, then press Check.