Factors · Least common multiple · 5.3

LCM by primes.

Using prime factorization: the LCM takes the HIGHEST power of every prime that appears. 8 = 2³, 12 = 2²×3 → take 2³ and 3¹ → 8×3 = 24.

01 / THE IDEA

See it work.

Factor tree

Split until every leaf is prime.

The prime leaves are the prime factorization.

82422

8 = 2³

Watch the method

LCM by primes

8 = 2³, 12 = 2²×3 → LCM = 2³×3 = 24.

1 / 2
LCM(8, 12)\text{LCM}(8,\, 12)
1

Prime factorize both

Find each number’s prime factorization.

8=23,  12=22×38 = 2^{3},\; 12 = 2^{2} \times 3
2

Take the highest power of each prime

Multiply the highest power of every prime that appears.

LCM=24\text{LCM} = 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.

Highest powers

Factor both into primes; for every prime that appears in either, take the larger exponent, then multiply.

Why it works

max(2³, 2²) = 2³, and 3¹.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the LCM of 4 and 3.

1

Prime factorize both

Find each number’s prime factorization. 4 = 2^2, 3 = 3

2

Take the highest power of each prime

Multiply the highest power of every prime that appears. LCM = 12

EX 2medium

Find the LCM of 6 and 9.

1

Prime factorize both

Find each number’s prime factorization. 6 = 2 × 3, 9 = 3^2

2

Take the highest power of each prime

Multiply the highest power of every prime that appears. LCM = 18

EX 3hard

Find the LCM of 5 and 6.

1

Prime factorize both

Find each number’s prime factorization. 5 = 5, 6 = 2 × 3

2

Take the highest power of each prime

Multiply the highest power of every prime that appears. LCM = 30

04 / COMMON TRAPS

Where students slip.

Trap

Taking the lowest power.

Fix

LCM uses the HIGHEST power (lowest is for the GCF).

Trap

Forgetting a prime in only one number.

Fix

Include every prime that appears in either.

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?
  • Prime factorize both.
  • Take the highest power of every prime.
C2

Find the LCM of 6 and 9.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.
C3

Find the LCM of 2 and 4.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.
C4

Find the LCM of 8 and 6.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.
Apply

Apply (4)

A1

Find the LCM of 8 and 9.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.
A2

Find the LCM of 3 and 9.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.
A3

Find the LCM of 6 and 4.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.
A4

Find the LCM of 4 and 6.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.
Extension

Extension (4)

E1

Find the LCM of 5 and 4.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.
E2

Find the LCM of 5 and 4.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.
E3

Find the LCM of 2 and 3.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.
E4

Find the LCM of 5 and 8.

Need a hint?
  • Prime factorize both.
  • Take the highest power of every prime.