Worked Example • Even Triple

LCM of 4, 6, and 8 (Equals 24)

The Least Common Multiple of 4, 6, and 8 is 24. Because 4 already divides evenly into 8, and LCM(6, 8) = 24, the smallest multiple shared by all three is 24.

LCM of 4, 6, and 8 Result

LCM(4, 6, 8) = 24

Greatest Common Factor: GCF(4, 6, 8) = 2

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

24 ÷ 4 = 624 ÷ 6 = 424 ÷ 8 = 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.

4 = 2 × 2

= 2²

6 = 2 × 3

= 2 × 3

8 = 2 × 2 × 2

= 2³

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

Prime	In 4	In 6	In 8	Highest Power
2	2²	2¹	2³	2³ = 8
3	—	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 4, 6, and 8

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(4, 6, 8) = 24:

Method A: Prime Factorization

• 4 = 2²
• 6 = 2 × 3
• 8 = 2³

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

Method B: GCF & Exact Division Check

The Greatest Common Factor of 4, 6, and 8 is 2.

24 ÷ 4 = 6 (remainder 0 ✓)

24 ÷ 6 = 4 (remainder 0 ✓)

24 ÷ 8 = 3 (remainder 0 ✓)

Real-World & Fraction Context

Three shift timers set for 4 hours, 6 hours, and 8 hours all ring together every 24 hours (once per day).

Mistake to Watch Out For

A very common mistake is dividing 4 × 6 × 8 = 192 by GCF(4, 6, 8) = 2 to get 96. That fails because 4 and 8 share an extra factor of 4!