Fractions
Prime factor trees
Break composite numbers into factor pairs until every branch ends in a prime, retaining repeated factors.
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Find the least common multiple
Find the smallest positive multiple shared by two numbers and use it to plan common-denominator work.
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List multiples or compare prime factors to find the smallest positive number divisible by both given numbers. Check both divisions before writing the result.
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What this activity builds
Identify the first positive shared multiple without confusing multiples with factors.
Worked example
What is the least common multiple of 6 and 8?
24.
The multiples of 6 begin 6, 12, 18, 24, while those of 8 begin 8, 16, 24. Their first positive match is 24. This makes twenty-fourths a useful common unit for sixths and eighths.
Teaching notes
Make the practice count
- Label the two multiple lists so factors are not substituted accidentally.
- Use the product of the two numbers as a possible common multiple, then check whether a smaller one works.
- Connect the result to renaming fractions rather than teaching it only as an isolated list exercise.
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