HCF or LCM: choosing the wrong one
Your child finds the highest common factor when the question needs the lowest common multiple, or the reverse. Both calculations are correct; the choice is wrong. These word problems are usually 2 marks, and the wrong choice usually costs both.
What it looks like
Bus A leaves the interchange every 12 minutes and Bus B leaves every 18 minutes. Both buses left the interchange together at 7.00 a.m. When is the next time both buses will leave together?
- Multiples of 12: 12, 24, 36, 48, ...
- Multiples of 18: 18, 36, 54, ...
- Lowest common multiple: 36
- 36 minutes after 7.00 a.m. is 7.36 a.m.
Why 7.06 a.m. is wrong: The HCF of 12 and 18 (6) was used instead of the LCM (36), giving 6 minutes after 7.00 a.m.
Why children do it
- Both methods use the same two numbers and similar working, so children pick the one they remember first.
- Word problems do not say "HCF" or "LCM"; your child has to decide from the story.
- "Common" appears in both names, so the labels themselves are easy to swap.
How to fix it at home
- Ask: "Are we waiting for something to happen again (multiple, LCM) or cutting something into equal groups (factor, HCF)?"
- Check the answer: 6 minutes is shorter than both bus gaps, so both buses cannot have left again by then.
- Have your child list the first few multiples or factors before using a shortcut, so the choice is visible.
Questions parents ask
What is the quickest way to tell HCF and LCM questions apart?
Repeating events (bells, buses, lights flashing) need the LCM. Sharing or cutting into the largest equal groups needs the HCF.
Is the HCF always smaller than the numbers?
It is never larger than the smaller number, and the LCM is never smaller than the larger number. Your child can use this to check every answer.
Where it shows up
Other careless mistakes
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