How to teach greatest common factor and lowest common multiple
Grade 4 to Grade 6
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.
How to teach it
- 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.
Worked example
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
Common mistakes
- 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).
Frequently asked questions
What are the greatest common factor and lowest common multiple?
The greatest common factor, or GCF, of two numbers is the largest number that divides into both. The lowest common multiple, or LCM, is the smallest number both divide into. For 12 and 18 the GCF is 6 and the LCM is 36.
What age or grade are GCF and LCM taught?
GCF and LCM are usually taught from Grade 4 to Grade 6, once factors and multiples are secure. They are used for simplifying and adding fractions, so they tend to appear alongside fraction work in the upper primary grades.
What are the GCF and LCM of 12 and 18?
The GCF is 6 and the LCM is 36. The factors common to 12 and 18 are 1, 2, 3 and 6, so the greatest is 6. The first multiple both share is 36, so that is the lowest common multiple.
How do you find the GCF and LCM?
For the GCF, list the factors of each number, ring the ones in both, and take the largest. For the LCM, list the multiples of each until one appears in both lists, and take the smallest. Prime factorisation is a faster method once the listing approach is understood.
What is the difference between factors and multiples here?
Factors are what goes into a number and run down towards 1, while multiples are what a number goes into and run up forever. GCF works with factors and LCM with multiples, so keeping the two words straight is essential to avoid swapping the answers.
Why does my child confuse GCF and LCM?
Because they are opposite directions of the same idea, children often give a multiple when the greatest common factor is wanted, or the reverse. They may also take a common factor that is not the greatest, or stop a multiples list too early and miss the first shared value.
What are GCF and LCM used for?
The GCF is used to simplify fractions and to share things into equal groups, while the LCM is used to find a common denominator when adding fractions and to work out when repeating events line up. Showing a real use for each makes the difference between them memorable.
Practise with free worksheets
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