Factors · Multiples · 2.3

Common multiples.

A common multiple appears in both numbers’ multiple lists. 4: 4, 8, 12, 16, … and 6: 6, 12, 18, … share 12, 24, … The smallest shared one is the least common multiple.

01 / THE IDEA

See it work.

Watch the method

Common multiples

4 and 6 share 12, 24, … — the LCM is 12.

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LCM(4, 6)\text{LCM}(4,\, 6)
1

List multiples of each

Multiples of 4 and of 6.

4,8,12,16  ∣  6,12,18,244,8,12,16\;\mid\; 6,12,18,24
2

The least common one

The smallest multiple they share is the LCM.

LCM(4,6)=12\text{LCM}(4,6) = 12
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 6.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

In both lists

List multiples of each and find the values they share; the smallest is the LCM.

Why it works

12 is the first multiple of both 4 and 6.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the LCM of 8 and 3.

1

List multiples of each

Multiples of 8 and of 3. 8,16,24,32 | 3,6,9,12

2

The least common one

The smallest multiple they share is the LCM. LCM(8,3) = 24

EX 2medium

Find the LCM of 5 and 6.

1

List multiples of each

Multiples of 5 and of 6. 5,10,15,20 | 6,12,18,24

2

The least common one

The smallest multiple they share is the LCM. LCM(5,6) = 30

EX 3hard

Find the LCM of 3 and 9.

1

List multiples of each

Multiples of 3 and of 9. 3,6,9,12 | 9,18,27,36

2

The least common one

The smallest multiple they share is the LCM. LCM(3,9) = 9

04 / COMMON TRAPS

Where students slip.

Trap

Stopping the lists too soon.

Fix

List far enough to find a shared value.

Trap

Picking any common one as “least”.

Fix

The LCM is the SMALLEST shared multiple.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Find the LCM of 2 and 3.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
C2

Find the LCM of 8 and 9.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
C3

Find the LCM of 2 and 3.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
C4

Find the LCM of 8 and 10.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
Apply

Apply (4)

A1

Find the LCM of 5 and 3.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
A2

Find the LCM of 8 and 10.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
A3

Find the LCM of 5 and 9.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
A4

Find the LCM of 3 and 9.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
Extension

Extension (4)

E1

Find the LCM of 2 and 4.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
E2

Find the LCM of 2 and 10.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
E3

Find the LCM of 2 and 8.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.
E4

Find the LCM of 3 and 10.

Need a hint?
  • List multiples of both numbers.
  • Find the smallest they share.