Primary 4 Maths: Factors, Multiples, HCF and LCM

Primary 4 Maths: Factors, Multiples, HCF and LCM — Tutor Lesson Plan

2026-10-27

Tutor lesson-prep guides · Primary maths

Students can list factors but swap HCF and LCM. This lesson separates them with one line: HCF multiplies the left column, LCM multiplies the left column and the bottom row.

Objectives — the student can list all factors of a number systematically, tell primes from composites, and find HCF and LCM by short division without mixing them up.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Times tables	7 × 8	56
Divisibility	Is 36 divisible by 4?	Yes, 36 ÷ 4 = 9
Division	48 ÷ 6	8

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Arrays	Arrange 12 tiles into every rectangle	Find 1×12, 2×6, 3×4
6-16 min	List factors	Write factors in pairs from the outside in	List the six factors of 12
16-26 min	Primes	Test 2, 3, 5, 7 on given numbers	Classify 9, 11, 15
26-36 min	HCF and LCM	Short division for both, side by side	One of each
36-42 min	Fix errors	Board HCF with the bottom row included	Name the extra row
42-45 min	Exit check	Three questions marked at once	Finish alone

03 Teaching script (read it out)

Scene 1: A factor is a rectangle you can make

12 tiles can be 1 row of 12, 2 rows of 6, 3 rows of 4.
Each arrangement gives a pair of factors: 1 and 12, 2 and 6, 3 and 4.

Student lists the factors of 18 the same way: 1, 2, 3, 6, 9, 18.

Scene 2: HCF is the biggest shared factor

The shared factors of 12 and 18 are 1, 2, 3 and 6, so the HCF is 6.
In short division the shared factors are in the left column: multiply only that column.

Student says “HCF looks at the left column only”.

Scene 3: LCM is the first shared multiple

Multiples of 4: 4, 8, 12, 16…; of 6: 6, 12, 18…
The first shared one is 12, which is the LCM. In short division, multiply the left column and the bottom row.

Warn: teach both sentences together, otherwise the two get swapped.

04 Question types and worked steps

Type	Example	Steps	Answer
List factors	24	Pairs: 1×24, 2×12, 3×8, 4×6	1, 2, 3, 4, 6, 8, 12, 24 (eight)
Prime test	9, 11, 15	Only test 2, 3, 5, 7	Only 11 is prime
HCF	12 and 18	Left column only	6
LCM	4 and 6	Left column and bottom row	12

Sanity check (teach this): The HCF can never exceed the smaller number, and the LCM can never be below the larger one; an HCF bigger than both numbers is a multiplication error.

05 Independent practice (3 questions)

Question	Answer	What to watch
HCF of 16 and 24	8	Left column only
LCM of 6 and 9	18	Left column and bottom row
How many factors has 24?	8	Neither 1 nor 24 missing

06 Common mistakes and what to say

Mistake	Student writes	Say this
Missing 1 or the number	lists 2, 3, 4, 6, 8, 12	Work in pairs from the outside in.
Thinking 1 is prime	answers “1 is prime”	A prime has exactly two factors; 1 has one.
HCF and LCM swapped	HCF found with the bottom row	HCF is the left column only.
Dividing one side only	12 divided by 2 but not 18	Divide both numbers at every step.

07 Homework (paper, section and question numbers)

Primary 4 first-term paper — Section B, questions 1 to 4
Primary 4 first-term paper — Section E, questions 1 and 2

08 Exit check (last 5 minutes)

Question	Answer	Decision
HCF of 16 and 24	8	All right: move to equivalent fractions
LCM of 6 and 9	18	One wrong: re-teach the two sentences
Number of factors of 24	8	Two wrong: repeat the array activity

09 Tutor FAQ

Is short division compulsory?

It is fastest for HCF and LCM, but start with listing if the concept is shaky.

Do they need the word coprime?

No. “No common factor except 1” is enough at this level.

What do word problems look like?

Sharing two things equally (HCF) and events happening together again (LCM).

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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.