Factors · Least common multiple · 5.1

The least common multiple.

The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. For 4 and 6, the shared multiples are 12, 24, … and the LCM is 12.

01 / THE IDEA

See it work.

Watch the method

The least common multiple

LCM(4, 6) = 12, the smallest shared multiple.

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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.

Smallest shared

Among all the multiples both numbers share, the LCM is the smallest.

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 4 and 9.

1

List multiples of each

Multiples of 4 and of 9. 4,8,12,16 | 9,18,27,36

2

The least common one

The smallest multiple they share is the LCM. LCM(4,9) = 36

EX 2medium

Find the LCM of 3 and 6.

1

List multiples of each

Multiples of 3 and of 6. 3,6,9,12 | 6,12,18,24

2

The least common one

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

EX 3hard

Find the LCM of 2 and 9.

1

List multiples of each

Multiples of 2 and of 9. 2,4,6,8 | 9,18,27,36

2

The least common one

The smallest multiple they share is the LCM. LCM(2,9) = 18

04 / COMMON TRAPS

Where students slip.

Trap

Multiplying the two numbers always.

Fix

4×6 = 24, but the LCM is 12 — find the smallest shared multiple.

Trap

Confusing LCM with GCF.

Fix

LCM is a multiple (bigger); GCF is a factor (smaller).

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 6 and 10.

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

Find the LCM of 4 and 9.

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

Find the LCM of 4 and 6.

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

Find the LCM of 6 and 10.

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

Apply (4)

A1

Find the LCM of 5 and 6.

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

Find the LCM of 5 and 6.

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

Find the LCM of 3 and 6.

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

Find the LCM of 8 and 9.

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

Extension (4)

E1

Find the LCM of 6 and 3.

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

Find the LCM of 3 and 6.

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

Find the LCM of 6 and 8.

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

Find the LCM of 3 and 9.

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