Factors · Least common multiple · 5.2

LCM by listing.

List the multiples of each number until you find one in both lists. 6: 6, 12, 18, 24, … 8: 8, 16, 24, … The first shared multiple, 24, is the LCM.

01 / THE IDEA

See it work.

Watch the method

LCM by listing

LCM(6, 8) = 24 (first shared multiple).

1 / 2
LCM(6, 8)\text{LCM}(6,\, 8)
1

List multiples of each

Multiples of 6 and of 8.

6,12,18,24  ∣  8,16,24,326,12,18,24\;\mid\; 8,16,24,32
2

The least common one

The smallest multiple they share is the LCM.

LCM(6,8)=24\text{LCM}(6,8) = 24
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.

First match

Write multiples of each in order; the first value that appears in both lists is the LCM.

Why it works

24 is the first multiple of both 6 and 8.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the LCM of 6 and 8.

1

List multiples of each

Multiples of 6 and of 8. 6,12,18,24 | 8,16,24,32

2

The least common one

The smallest multiple they share is the LCM. LCM(6,8) = 24

EX 2medium

Find the LCM of 6 and 9.

1

List multiples of each

Multiples of 6 and of 9. 6,12,18,24 | 9,18,27,36

2

The least common one

The smallest multiple they share is the LCM. LCM(6,9) = 18

EX 3hard

Find the LCM of 2 and 3.

1

List multiples of each

Multiples of 2 and of 3. 2,4,6,8 | 3,6,9,12

2

The least common one

The smallest multiple they share is the LCM. LCM(2,3) = 6

04 / COMMON TRAPS

Where students slip.

Trap

Stopping the lists too early.

Fix

Keep listing until a shared multiple appears.

Trap

Picking a later common multiple.

Fix

The LCM is the FIRST shared one.

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 8 and 3.

Need a hint?
  • List multiples of each.
  • Take the first they share.
C2

Find the LCM of 3 and 4.

Need a hint?
  • List multiples of each.
  • Take the first they share.
C3

Find the LCM of 3 and 6.

Need a hint?
  • List multiples of each.
  • Take the first they share.
C4

Find the LCM of 3 and 6.

Need a hint?
  • List multiples of each.
  • Take the first they share.
Apply

Apply (4)

A1

Find the LCM of 3 and 9.

Need a hint?
  • List multiples of each.
  • Take the first they share.
A2

Find the LCM of 8 and 3.

Need a hint?
  • List multiples of each.
  • Take the first they share.
A3

Find the LCM of 4 and 6.

Need a hint?
  • List multiples of each.
  • Take the first they share.
A4

Find the LCM of 5 and 9.

Need a hint?
  • List multiples of each.
  • Take the first they share.
Extension

Extension (4)

E1

Find the LCM of 4 and 6.

Need a hint?
  • List multiples of each.
  • Take the first they share.
E2

Find the LCM of 5 and 4.

Need a hint?
  • List multiples of each.
  • Take the first they share.
E3

Find the LCM of 6 and 10.

Need a hint?
  • List multiples of each.
  • Take the first they share.
E4

Find the LCM of 8 and 3.

Need a hint?
  • List multiples of each.
  • Take the first they share.