Worked Example • Shared Factor of 6

LCM of 18 and 24 (Equals 72)

The Least Common Multiple of 18 and 24 is 72. Because 18 (2 × 3²) and 24 (2³ × 3) have a Greatest Common Factor of 6, their LCM is (18 × 24) ÷ 6 = 72.

LCM of 18 and 24 Result

LCM(18, 24) = 72

Greatest Common Factor: GCF(18, 24) = 6

Check the answer (every division leaves a remainder of 0):

72 ÷ 18 = 472 ÷ 24 = 3

Show the Working (Step-by-Step)

Switch method in one click:

Step 1: Break each number down into its prime factors.

Write each input as a product of prime numbers, then group matching primes with exponents.

18 = 2 × 3 × 3

= 2 × 3²

24 = 2 × 2 × 2 × 3

= 2³ × 3

Step 2: For each prime, pick the highest exponent that appears in any single number.

Prime	In 18	In 24	Highest Power
2	2¹	2³	2³ = 8
3	3²	3¹	3² = 9

Step 3: Multiply those highest prime powers together to get the LCM.

LCM = 2³ × 3² = 8 × 9 = 72

Full Written Solution for the LCM of 18 and 24

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(18, 24) = 72:

Method A: Prime Factorization

• 18 = 2 × 3²
• 24 = 2³ × 3

Multiply the highest power of each prime: 2³ × 3² = 72.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 18 and 24 is 6.

72 ÷ 18 = 4 (remainder 0 ✓)

72 ÷ 24 = 3 (remainder 0 ✓)

Real-World & Fraction Context

Floor tiles sold in packs of 18 and trim pieces sold in packs of 24 match evenly at 72 pieces (4 packs of tiles and 3 packs of trim).

Mistake to Watch Out For

Don't stop at 36 (24 does not divide evenly into 36—36 ÷ 24 = 1.5).