Grade 6: GCF & LCM

Warm up with a quick recall on the board. List factors (for the highest common factor) or multiples (for the lowest common multiple) of each number and find the shared one. Later use prime factors.

The greatest common factor (GCF) of two numbers is the largest number that divides into both. The lowest common multiple (LCM) is the smallest number both divide into. For 12 and 18 the GCF is 6 and the LCM is 36. The two are opposite directions, factors run down and stop, multiples run up and never end, so students need factors and multiples secure first. Model the method clearly, thinking aloud:

• Keep the words straight: factors are what goes into a number, multiples are what a number goes into.
• For the GCF, list the factors of each number, ring the ones in both, and take the largest.
• For the LCM, list multiples of each number until one appears in both lists, and take the smallest.
• Show a real use for each: GCF for simplifying fractions and sharing into equal groups, LCM for adding fractions and repeating events lining up.
• Introduce prime factorisation later as a faster method once the listing method is understood.

Work this through step by step on the board, then have the class talk you through a second one.

• For 12 and 18:
• factors of 12: 1, 2, 3, 4, 6, 12
• factors of 18: 1, 2, 3, 6, 9, 18
• common: 1, 2, 3, 6 -> GCF = 6
• multiples of 12: 12, 24, 36, 48
• multiples of 18: 18, 36, 54
• first shared -> LCM = 36

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the worksheet independently. Hand out the three difficulty levels below so every child works at the right stretch.

Circulate and look for these, they are the usual sticking points:

• Swapping the two, giving a multiple when the greatest common factor is wanted.
• Taking a common factor that is not the greatest (choosing 3 instead of 6 for 12 and 18).
• Stopping the multiples lists too early and missing the first shared value.
• Thinking the LCM is always the two numbers multiplied together (it is only when they share no factors).
• Mixing up which to list (factors vs multiples), and stopping before finding the common value.

Pull the class back together. Ask one child to explain gcf & lcm in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.