Worked Example • High-Frequency Fraction Pair

LCM of 6 and 8 (Equals 24)

The Least Common Multiple of 6 and 8 is 24. Because 6 (2 × 3) and 8 (2³) share a Greatest Common Factor of 2, their LCM is (6 × 8) ÷ 2 = 24 rather than 48.

LCM of 6 and 8 Result

LCM(6, 8) = 24

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

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

24 ÷ 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.

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 6	In 8	Highest Power
2	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 6 and 8

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

Method A: Prime Factorization

• 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 6 and 8 is 2.

24 ÷ 6 = 4 (remainder 0 ✓)

24 ÷ 8 = 3 (remainder 0 ✓)

Real-World & Fraction Context

Because a day has 24 hours, medications or shift checks ordered every 6 hours (4 times a day) and every 8 hours (3 times a day) realign at the exact same hour every 24 hours.

Mistake to Watch Out For

Multiplying 6 × 8 = 48 doubles the necessary denominator. Always check 8 × 1 = 8, 8 × 2 = 16, 8 × 3 = 24 first.