Worked Example • Most-Searched Classroom Pair

LCM of 8 and 12 (Equals 24)

The Least Common Multiple of 8 and 12 is 24. Because 8 and 12 share a Greatest Common Factor of 4, their LCM is (8 × 12) ÷ 4 = 24.

LCM of 8 and 12 Result

LCM(8, 12) = 24

Greatest Common Factor: GCF(8, 12) = 4

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

24 ÷ 8 = 324 ÷ 12 = 2

Show the Working (Step-by-Step)

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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.

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 8	In 12	Highest Power
2	2³	2²	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 8 and 12

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

Method A: Prime Factorization

• 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 8 and 12 is 4.

24 ÷ 8 = 3 (remainder 0 ✓)

24 ÷ 12 = 2 (remainder 0 ✓)

Real-World & Fraction Context

Beverage cans sold in 8-packs and 12-packs match up at 24 cans (three 8-packs or two 12-packs).

Mistake to Watch Out For

Students who only divide by 2 instead of the full GCF of 4 accidentally write 48. Always check if half of 48 (24) is still divisible by both 8 and 12.