Distinguish Greatest Common Factor from Least Common Multiple
For a greatest common factor, list divisors of both targets and choose the largest shared one.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: For 18 and 24, shared factors are one, two, three, six, so GCF is six.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Common factors divide both numbers; common multiples contain both as whole-number factors. The greatest common factor helps make the largest identical groups, while the least common multiple helps find the first shared repeat point. They answer different questions, so list the right type of quantities.
For a greatest common factor, list divisors of both targets and choose the largest shared one. For a least common multiple, list positive multiples and choose the smallest shared one. Explain the chosen list before calculating.
Name factor or multiple before making a list. GCF and LCM cannot be interchanged even when the target numbers are identical. Make two clearly labeled lists and mark their common entries.
- Make two clearly labeled lists and mark their common entries.
- Work through the supplied example and label what each number or attribute represents.
- For a greatest common factor, list divisors of both targets and choose the largest shared one.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
For 18 and 24, shared factors are one, two, three, six, so GCF is six. For repeat cycles of six and eight, common multiples include twenty-four, forty-eight, so LCM is twenty-four. A largest divisor and smallest shared repeat are different operations. Name factor or multiple before making a list. GCF and LCM cannot be interchanged even when the target numbers are identical. Make two clearly labeled lists and mark their common entries.
Check your reasoning
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Helpful tips
- Name factor or multiple before making a list.
- GCF and LCM cannot be interchanged even when the target numbers are identical.
See the answer and explanation
4
Use common divisors for GCF and common positive multiples for LCM. The result is 4.
Take it further
Find GCF(24,36)=12 and LCM(8,12)=24. Explain the different lists.
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More practice: try new cases
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