Worked Example • Standard 3-Fraction Triple

LCM of 6, 8, and 12 (Equals 24)

The Least Common Multiple of 6, 8, and 12 is 24. Both 6 and 12 divide cleanly into 24 (24 ÷ 6 = 4 and 24 ÷ 12 = 2), and 8 × 3 = 24.

LCM of 6, 8, and 12 Result

LCM(6, 8, 12) = 24

Greatest Common Factor: GCF(6, 8, 12) = 2

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

24 ÷ 6 = 424 ÷ 8 = 324 ÷ 12 = 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

8 = 2 × 2 × 2

= 2³

12 = 2 × 2 × 3

= 2² × 3

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

Prime	In 6	In 8	In 12	Highest Power
2	2¹	2³	2²	2³ = 8
3	3¹	—	3¹	3¹ = 3

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

LCM = 2³ × 3¹ = 8 × 3 = 24

Full Written Solution for the LCM of 6, 8, and 12

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(6, 8, 12) = 24:

Method A: Prime Factorization

• 6 = 2 × 3
• 8 = 2³
• 12 = 2² × 3

Multiply the highest power of each prime: 2³ × 3¹ = 24.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 6, 8, and 12 is 2.

24 ÷ 6 = 4 (remainder 0 ✓)

24 ÷ 8 = 3 (remainder 0 ✓)

24 ÷ 12 = 2 (remainder 0 ✓)

Real-World & Fraction Context

When baking tarts with shell trays of 6, filling jars of 8, and glaze packets of 12, baking 24 tarts uses 4 trays, 3 jars, and 2 packets with zero leftovers.

Mistake to Watch Out For

Do not multiply 6 × 8 × 12 = 576, and don't stop at 12 (since 8 does not divide evenly into 12).