Primary 4 · Mathematics
P4 factors and multiples
HCF and LCM come from the same two numbers and sound almost alike, so the hard part is not the working, it is choosing the right one. Here is how to tell which a question wants.
- Level
- P4
- Usually taught
- Term 1
- Covers
- 4 concepts
What changes at P4
In Primary 4, your child learns factors (numbers that divide into a number exactly) and multiples (the numbers you reach by counting up in it), and then the two that catch people out: the highest common factor (HCF) and the lowest common multiple (LCM).
HCF and LCM sound alike and both "find something in common", so the real skill is not the working, it is choosing the right one. HCF splits into the biggest equal groups; LCM finds when two things line up again.
The sentence that costs the mark
Two ribbons are 12 cm and 18 cm long. Each is cut into equal pieces, as long as possible. How long is each piece?
What the working usually does
LCM of12 and 18=36 cm
Takes the lowest common multiple, when the two lengths next line up. It is a real answer, just to a different question.
What the question asked
HCF of12 and 18=6 cm
Takes the highest common factor, the longest length that divides both exactly. That is what "equal pieces, as long as possible" is asking for.
Both are real numbers you can work out from 12 and 18, and a child who can find both may still pick the wrong one. The tell is a sense-check: a piece cut from an 18 cm ribbon cannot be 36 cm, so the LCM was never possible here.
| ÷ by | 12 | 18 |
|---|---|---|
| 2 | 6 | 9 |
| 3 | 2 | 3 |
The same question, worked properly
Read what the question wants
longest equal piece = HCF, not LCMThis is the step that fails. The pieces must divide 12 AND 18 exactly, and be as long as possible. That is the highest common factor. Reaching for the LCM here is where the mark goes.
Ladder 12 and 18
common factors 2 and 3, so HCF = 6Divide both by a common factor, again and again. 12 and 18 share 2, then 3. Multiply those factors: HCF = 2 × 3 = 6.
Answer, then sense-check
each piece = 6 cmEach piece is 6 cm, and 6 divides both 12 and 18 exactly. A quick check settles it: a piece cannot be longer than the ribbon, so 36 cm was never on.
How can you tell it has clicked?
Ask your child, in their own words, whether the question wants equal groups shared out (HCF) or when two things next meet (LCM). If they can say which, the working takes care of itself.
If they jump straight to a method without deciding that, the wrong one is a coin toss. The fix is one sense-check: HCF is never bigger than the numbers, LCM is never smaller.
One thing to try tonight
Use two numbers, 12 and 18: "what is the biggest equal share you can make from each, with none left over?" (that is HCF). Then a different question: "two buses leave every 12 and 18 minutes, when do they next leave together?" (that is LCM). Same numbers, opposite tool.
The point is not the arithmetic, which they can usually do. It is hearing the question and knowing which of the two it wants. Practise the choosing, not the laddering.
What your child will meet in this topic
- Factors and Multiples
- Prime Numbers
- Lowest Common Multiple
- Highest Common Factor
Most Singapore schools introduce this in Term 1, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.
What it leads to
HCF and LCM come back through fractions (a common denominator is an LCM; simplifying uses an HCF) and again in ratio. Getting the choice right here saves the same confusion turning up later wearing different clothes.
A child who can name which one a question wants tends to stay calm in P5 and P6, where the numbers are bigger and a wrong choice costs a whole multi-mark question.
The methods your child will use here
Each one is the same method wherever it turns up, so it is worth learning once.
More in Primary 4
Other topics in the same year, so you can see what sits either side of this one.
Struggling with the working rather than the topic itself? How to help your child with problem sums
See how your child is doing on this topic
StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.