Least common multiple (LCM) - How to find it

A common multiple is a number that sits in both times tables. The least common multiple is the first one. Listing is the most honest method at this age, because your child can watch the two lists meet.

The pairs are chosen with care. In 3 and 9, 4 and 8, and 6 and 18, the larger number is already a multiple of the smaller, so it is the answer. In 3 and 7, nothing is shared until their product, 21. And 9 and 12 share a factor of 3, so they meet early, at 36.

This is the LCM half of 6.NS.B.4, which asks for the least common multiple of two whole numbers up to 12. The pair 6 and 18 goes a little past that.

Start with the worked example at the top and treat it as a case to solve. Ask your child, "Is 12 a multiple of 4?" Then, "Is it on the list?" The list of multiples of 4 jumps from 8 to 16, and that missing 12 is why the example names 24. The true LCM of 3 and 4 is 12.

A note for you: the solution page also gives 108 for 9 and 12. The multiples of 9 run 9, 18, 27, 36, and 36 is also 12 x 3, so the LCM is 36.

Once the slips are found, the method holds up. Have your child say each multiple aloud and circle the first match.

The classic grocery store puzzle is pure LCM: hot dogs come in packs of 10, buns in packs of 8. Ask, "How many packs of each so nothing is left over?" The answer, 40 of each, means 4 packs of hot dogs and 5 packs of buns.

On a drive, watch two turn signals that blink at different speeds and count until they flash together.

Full House: An Invitation to Fractions by Dayle Ann Dodds, about an inn that fills up one guest at a time, is a gentle look at fractions of a whole, and fractions are where the LCM returns, once denominators differ.

Name the work: "You checked the list before you trusted the example." Next in this series, the word problems sheet hides the LCM inside a story.