Confusing HCF and LCM
"The HCF-LCM Swap"
The Mistake in Action
Find the HCF of 12 and 18.
Wrong: $12 = 2^2 \times 3$ $18 = 2 \times 3^2$ HCF = $2^2 \times 3^2 = 36$
Why It Happens
Students mix up whether to use the higher or lower powers, or confuse which one is "highest" and which is "lowest".
The Fix
HCF = Highest Common Factor
- Use only the factors that appear in both numbers
- Take the lower power of each
- HCF is always smaller than or equal to both numbers
LCM = Lowest Common Multiple
- Use all factors from both numbers
- Take the higher power of each
- LCM is always larger than or equal to both numbers
For 12 and 18:
- Common factors: 2 and 3
- Lower powers: $2^1$ and $3^1$
- HCF = $2 \times 3 = 6$
Spot the Mistake
Can you identify where this student went wrong?
Find the HCF of 12 and 18
$12 = 2^2 \times 3$, $18 = 2 \times 3^2$
HCF = $2^2 \times 3^2 = 36$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: