Primary 4 Maths — HCF and LCM: a Tutor Lesson-Prep Guide (short division, choosing the right one)

2026-11-10

Tutor lesson-prep guides · Primary maths

A pupil short-divides 18 and 24, gets 3 and 4, and says the highest common factor is 3. His hands did the right thing, but he does not know the left column must be multiplied. This lesson turns that into a fixed action.

Objectives — By the end the pupil can: (1) list the factors of 18 and of 24, circle 1, 2, 3 and 6, and say the highest is 6; (2) short-divide 18 and 24 together, multiply the 2 and 3 on the left to get 6, and multiply those by the 3 and 4 below to get 72; (3) choose HCF for the most groups possible and LCM for when two events next coincide, and say why.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Times tables 1 to 9	6 times 7	42
Meaning of a factor	Which numbers divide 12 exactly?	1, 2, 3, 4, 6, 12
Testing divisibility	Does 4 divide 36 exactly?	Yes, 36 divided by 4 is 9

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Error diagnosis	Write 18 and 24 and ask for the HCF, watching for the answer 3	Answers and explains the method
5-12 min	Listing	Have the pupil list the factors of both and circle the shared ones	Lists and circles 1, 2, 3, 6
12-22 min	Three-act teaching	Deliver the scripts on short division, multiplying the left column, and choosing HCF or LCM	Repeats: left column gives HCF, left times bottom gives LCM
22-32 min	Worked examples	Model one listing, one HCF, one LCM and one word problem	Copies one and writes both expressions
32-40 min	Independent practice	Hand out three questions and require the short division written down	Works alone and labels each answer HCF or LCM
40-45 min	Exit check	Collect the work and note whether the method or the choice failed	Says why he chose HCF or LCM

03 Teaching script (read it out)

Scene 1: Short division: left column gives HCF, left times bottom gives LCM

Write 18 and 24 side by side. Divide both by 2 to get 9 and 12, then both by 3 to get 3 and 4. Since 3 and 4 share no factor, stop. The divisors on the left, 2 and 3, multiply to 6, which is the highest common factor. For the lowest common multiple, multiply the left column and the numbers below: 2 times 3 times 3 times 4 is 72. Two sentences cover it: the left column gives the HCF, left times bottom gives the LCM.

Left column gives the HCF, left times bottom gives the LCM.

Scene 2: Telling them apart: cutting up uses HCF, piling up uses LCM

Problems come in two shapes. First: 24 sweets and 36 biscuits, what is the greatest number of identical packs? We are cutting both amounts into smaller equal parts, so we want a common factor, and the answer is 12. Second: bus A every 8 minutes and bus B every 12 minutes, when do they next leave together? We are piling time up, so we want a common multiple, and the answer is 24. One rule to remember: cutting up uses HCF, piling up uses LCM.

Cutting up uses HCF, piling up uses LCM.

Scene 3: Listing: three numbers need the union

Find the LCM of 4, 6 and 9. Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36. Of 6: 6, 12, 18, 24, 30, 36. Of 9: 9, 18, 27, 36. The first number present in all three lists is 36. Check by short division: divide 4, 6 and 9 by 2 to get 2, 3 and 9, then by 3 to get 2, 1 and 3; the left column 2 times 3, times 2 times 1 times 3 below, gives 36. Both methods must agree before the pupil really owns it.

With three numbers, all three must divide before you can divide.

04 Question types and worked steps

Type	Example	Steps	Answer
Listing	All common factors of 18 and 24	List factors of each and circle the shared ones	1, 2, 3, 6, so the HCF is 6
Short division for HCF	12 and 30	Divide both by 2 to get 6 and 15, then by 3 to get 2 and 5; left column 2 times 3	6
Short division for LCM	18 and 24	Divide by 2 then 3; left 2 times 3, times 3 and 4 below	72
Word problem	24 sweets and 36 biscuits, greatest number of identical packs	Cutting up, so HCF: divide by 2, 2, 3 to get 2 and 3; left column 12	12 packs, two sweets and three biscuits each

Sanity check (teach this): Sense check: the HCF can never exceed the smaller number, and 6 is below 18, so 6 is sensible. The LCM can never be below the larger number, and 72 exceeds 24, so 72 is sensible; an LCM smaller than 24 would be wrong. Also HCF times LCM equals the product of the numbers: 6 times 72 is 432 and 18 times 24 is 432, which is a useful check.

05 Independent practice (3 questions)

Question	Answer	What to watch
HCF	HCF of 18 and 24	6, from the left column 2 times 3
LCM	LCM of 18 and 24	72, left column times 3 and 4 below
Three numbers	LCM of 4, 6 and 9	36
Word problem	Bus A every 8 minutes, bus B every 12, when next together	After 24 minutes, which is the LCM

06 Common mistakes and what to say

Mistake	Student writes	Say this
Taking only one number from the left	Says the HCF of 18 and 24 is 3	Both the 2 and the 3 on the left must be multiplied. You took only the last divisor, so you got 3 instead of 6.
Swapping HCF and LCM	Finds 72 for the greatest number of packs	Packing means cutting up, and cutting up uses the HCF. Seventy-two packs is more than the 24 sweets you started with, so it cannot be right.
Stopping too early	Divides 12 and 30 by 2 once and answers 2	Both 12 and 30 still divide by 3, and while both divide you must keep going.
Forgetting that 1 is a common factor	Lists common factors as 2, 3, 6 only	One divides every number, so it is always a common factor and must appear in the list.

07 Homework (paper, section and question numbers)

Primary 4 factors and multiples practice — Section B, questions 1 to 4
Primary 4 HCF and LCM word problems — Section C, questions 1 and 2
Primary maths chapter index — All chapters in one table

08 Exit check (last 5 minutes)

Question	Answer	Decision
HCF of 18 and 24	6	Answering 3 means the left column was not multiplied; reteach act one
LCM of 18 and 24	72	Answering 12 means the two parts were mixed; redo the short division
Which one for the greatest number of packs?	The HCF	Answering LCM means the choice is not secure; reteach act two

09 Tutor FAQ

Is short division compulsory?

In Primary 4, listing comes first because it builds meaning. Short division is the speed tool. A pupil who can only short-divide will choose wrongly in word problems.

How is short division different with three numbers?

All three must divide at each step. For 4, 6 and 9 only 1 divides all three, so move straight to listing or handle them in pairs.

Are HCF and LCM related?

Yes: HCF times LCM equals the product of the two numbers. For 18 and 24, 6 times 72 is 432, exactly 18 times 24, which makes a good check.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.