Factors · Least common multiple · 5.4

LCM in the real world.

LCM answers “when do they line up again?” and gives the least common denominator for adding fractions. Two events every 4 and 10 minutes next coincide at the LCM, 20 minutes.

01 / THE IDEA

See it work.

Watch the method

LCM in the real world

Events every 4 and 10 min coincide at LCM = 20.

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LCM(4, 10)\text{LCM}(4,\, 10)
1

List multiples of each

Multiples of 4 and of 10.

4,8,12,16  ∣  10,20,30,404,8,12,16\;\mid\; 10,20,30,40
2

The least common one

The smallest multiple they share is the LCM.

LCM(4,10)=20\text{LCM}(4,10) = 20
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 6.

streak 0
best 0
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— / WHY IT WORKS

The idea underneath.

Lining up

When repeating cycles meet again, or fractions need a common denominator, the LCM is the tool. (Links to the Fractions subject — the LCD.)

Why it works

4 and 10 first coincide at 20.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the LCM of 6 and 10.

1

List multiples of each

Multiples of 6 and of 10. 6,12,18,24 | 10,20,30,40

2

The least common one

The smallest multiple they share is the LCM. LCM(6,10) = 30

EX 2medium

Find the LCM of 6 and 4.

1

List multiples of each

Multiples of 6 and of 4. 6,12,18,24 | 4,8,12,16

2

The least common one

The smallest multiple they share is the LCM. LCM(6,4) = 12

EX 3hard

Find the LCM of 4 and 10.

1

List multiples of each

Multiples of 4 and of 10. 4,8,12,16 | 10,20,30,40

2

The least common one

The smallest multiple they share is the LCM. LCM(4,10) = 20

04 / COMMON TRAPS

Where students slip.

Trap

Using the GCF for lining up.

Fix

Repeating/coinciding events → LCM.

Trap

Adding fractions without the LCD.

Fix

The common denominator is the LCM of the denominators.

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 3 and 10.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
C2

Find the LCM of 3 and 6.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
C3

Find the LCM of 2 and 8.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
C4

Find the LCM of 8 and 6.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
Apply

Apply (4)

A1

Find the LCM of 4 and 9.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
A2

Find the LCM of 2 and 3.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
A3

Find the LCM of 2 and 4.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
A4

Find the LCM of 8 and 6.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
Extension

Extension (4)

E1

Find the LCM of 2 and 8.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
E2

Find the LCM of 4 and 3.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
E3

Find the LCM of 5 and 10.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.
E4

Find the LCM of 5 and 6.

Need a hint?
  • “When do they line up?” → LCM.
  • The LCD is the LCM of the denominators.