KnowThisKey Takeaways
Key Takeaways
- 1LCM (least common multiple) is the smallest number two or more numbers both divide into evenly.
- 2HCF/GCD (highest common factor / greatest common divisor) is the largest number that divides evenly into two or more numbers.
- 3LCM helps you combine things (like adding fractions); HCF helps you split things (like simplifying fractions or dividing groups evenly).
The concept
You need to add the fractions 1/4 and 1/6. Which quantity tells you the smallest common denominator to use?
Worked examples
Example 1: Finding LCM by listing multiples (baseline case)
Example 2: Finding HCF of three numbers (edge/variation case)
Example 3: Two buses on different schedules (applied case)
Common mistakes
Common Mistakes
Using HCF when the problem actually calls for LCM, or vice versa.
→ Ask: am I combining/syncing things (LCM) or splitting/simplifying things (HCF)? The verb in the problem usually gives it away.
Assuming LCM is always the product of the two numbers.
→ That's only true when the numbers share no common factors. LCM(4,6)=12, not 24, because they share a factor of 2.
Forgetting the identity LCM × HCF = product of the numbers.
→ This shortcut lets you find either value instantly once you know the other and the two original numbers — useful for checking your work.
Common misconception
“HCF and GCD are two different concepts that happen to sound similar.”
They're exactly the same thing under two different names — HCF (Highest Common Factor) is more common in British/Indian curricula, GCD (Greatest Common Divisor) is more common in American ones. Same definition, same calculation, same answer.
Try it yourself
What to do next
What to do next
- Next time you add two fractions with different denominators, find the LCM of the denominators first — it's the fastest path to the answer.
- Practice the Euclidean algorithm on two numbers by hand — it's faster than factoring once numbers get into the hundreds.
- Use the LCM × HCF = a × b identity to double-check any LCM or HCF calculation you do.