Grade 6 · Unit 3 · Lesson 2

Greatest Common Factor and Least Common Multiple

Two long names for two simple questions. Break both numbers into primes, line them up, and circle the pairs. The pairs answer one question and the leftovers answer the other.

About 25 minutes NC.6.NS.4

Finn

Hi, I am Finn. Before anything else: these two names tell you exactly what they are. Nobody ever says that part out loud, which is why they feel like nonsense.

Read them slowly and they turn into ordinary questions. The rest of the lesson is one picture that answers both at once.

The whole method

Break both numbers into primes. Line the lists up and circle the pairs. One from each pair, multiplied, is the greatest common factor. One from each pair plus every leftover, multiplied, is the least common multiple. The pairs are what the two numbers share. The leftovers are what each one still needs.

The parts of this lesson

Seven short pages. Do them in order the first time.

1The VocabularyThe five words inside the two names, plus prime. Start here. 2Breaking a Number into Prime FactorsFactor trees. Split, keep splitting, circle it when it is prime. 3Factor FactsHow to tell what divides into a number without dividing. 4Finding the GCF and LCM from the Prime FactorsLine the two lists up, circle the pairs, and read both answers off. 5Worked ExamplesWhy it took all of them, then the whole thing again with 18 and 30. 6Why Do We Need This?Reducing a fraction in one step, and the common denominator. 7Practice ProblemsThirteen of them, with a hint, a next step and the answer on each.

Where this goes next

Back to the 6th grade mapEvery unit of the year, in order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.