Worked Example • Multiples of 3

LCM of 6 and 9 (Equals 18)

The Least Common Multiple of 6 and 9 is 18. Both 6 and 9 are multiples of 3 (GCF = 3), so dividing their product (6 × 9 = 54) by 3 gives LCM(6, 9) = 18.

LCM of 6 and 9 Result

LCM(6, 9) = 18

Greatest Common Factor: GCF(6, 9) = 3

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

18 ÷ 6 = 318 ÷ 9 = 2

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.

6 = 2 × 3

= 2 × 3

9 = 3 × 3

= 3²

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

Prime	In 6	In 9	Highest Power
2	2¹	—	2¹ = 2
3	3¹	3²	3² = 9

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

LCM = 2¹ × 3² = 2 × 9 = 18

Full Written Solution for the LCM of 6 and 9

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(6, 9) = 18:

Method A: Prime Factorization

• 6 = 2 × 3
• 9 = 3²

Multiply the highest power of each prime: 2¹ × 3² = 18.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 6 and 9 is 3.

18 ÷ 6 = 3 (remainder 0 ✓)

18 ÷ 9 = 2 (remainder 0 ✓)

Real-World & Fraction Context

When adding 5/6 + 2/9, using LCD(6, 9) = 18 gives 15/18 + 4/18 = 19/18 (or 1 1/18), three times smaller than using 54.

Mistake to Watch Out For

Don't multiply 6 × 9 = 54. Because both numbers sit in the 3-times table, they share a factor of 3.