Fractions
Find the greatest common factor
Find the greatest common factor of positive integer pairs. Choose a maximum of 24, 40, 60 or 120 and 10, 15 or 20 questions, with a separate answer key.
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LCM and GCF of two or three numbers
Find the least common multiple and greatest common factor side by side. Choose two or three numbers per set, ranges through 120, and 10 or 12 questions.
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For every set, find both the least common multiple and greatest common factor. Write each result under its matching column heading.
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Learning objective
What this activity builds
Use the same number set to distinguish shared divisors from shared multiples and select the correct extreme in each case.
Worked example
Find the LCM and GCF of 12, 18 and 30.
LCM = 180; GCF = 6
12 = 2 × 2 × 3, 18 = 2 × 3 × 3 and 30 = 2 × 3 × 5. The common prime copies give 2 × 3 = 6. Using the greatest required count of each prime gives 2 × 2 × 3 × 3 × 5 = 180.
Teaching notes
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- The selected maximum limits the numbers in the question, not the answers. A least common multiple can be much larger than any input.
- For GCF, a factor must divide every number in the set. For LCM, every input must divide the proposed answer.
- When working with three numbers, do not stop after comparing only the first pair. Include the third number in both calculations.
- A GCF of 1 is valid for numbers with no larger common factor. The LCM still exists; use every prime power required by the set.
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