Prime factorisation for LCM
To find the LCM by prime factorisation, write both numbers as primes and take every prime that appears in either number, using the highest power needed.
Practice This ConceptMain explanation
Teacher explanation
The LCM is the smallest common multiple, so it must contain enough prime factors to cover both numbers completely. That is why we choose the greatest power of each prime appearing in either number, not the smallest one.
Example
36 = 2^2 x 3^2 and 48 = 2^4 x 3, so the LCM is 2^4 x 3^2 = 144.
Simple analogy
For LCM, build upward with the biggest prime powers.
Common confusion
Students take the smallest powers and end up finding the HCF instead of the LCM.
Exam tip
For LCM, remember the phrase: all primes with maximum powers.
Answer writing and exam use
1-mark use
Write the exact meaning of prime factorisation for lcm in one clean line.
2-mark use
Define prime factorisation for lcm and add one example or condition.
3-mark use
Explain prime factorisation for lcm, show the method or example, and mention the common mistake.
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