Sixth Grade · Math · week 16

Greatest common factor and least common multiple

Find the GCF and LCM of two whole numbers and use them to simplify fractions and find common denominators.

The greatest common factor (GCF) of two numbers is the largest number that divides evenly into both. List the factors of each number, then find the biggest one they share.

The least common multiple (LCM) is the smallest number that both numbers divide into evenly. List multiples of each number until you find one they share.

GCF is useful for simplifying fractions - divide the numerator and denominator by their GCF. LCM is useful for finding a common denominator when adding or subtracting fractions.

📋 For the teacher
Teach it (10–15 min):
  • List factors and multiples together on paper, circling the shared ones - the visual match makes GCF and LCM click.
  • Connect GCF directly to simplifying fractions: "the GCF is exactly the number you divide the top and bottom by."
  • Connect LCM directly to adding fractions with unlike denominators: "the LCM becomes your common denominator."
  • Start with small, friendly number pairs before trying larger ones.
Talk about it:
  • What is the difference between GCF and LCM in your own words?
  • How does GCF help you simplify a fraction in one step instead of several?
  • How does LCM help when adding fractions with different denominators?

Mastery looks like: They find the GCF and LCM of two numbers by listing, and apply GCF to simplify a fraction and LCM to find a common denominator.

Common stumbles: Confusing GCF and LCM, such as picking the smallest shared factor or the largest shared multiple by mistake; stopping the multiples list too early and missing the true LCM.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

MultiplicationEqual groups and arrays make products finally click.try →FractionsSlice bars and circles into equal parts and compare them.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
← Back to todayAll coursesYear planner