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Worked Example • Homepage Benchmark Triple

LCM of 12, 18, and 24 (Equals 72)

The Least Common Multiple of 12, 18, and 24 is 72, and their Greatest Common Factor is 6. Using prime exponents, 12 = 2² × 3¹, 18 = 2¹ × 3², and 24 = 2³ × 3¹, giving 2³ × 3² = 8 × 9 = 72.

2 to 10 integers • up to 18 digits each
Parsed:121824
LCM of 12, 18, and 24 Result
LCM(12, 18, 24) = 72
Greatest Common Factor: GCF(12, 18, 24) = 6
Check the answer (every division leaves a remainder of 0):
72 ÷ 12 = 672 ÷ 18 = 472 ÷ 24 = 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.

12 = 2 × 2 × 3
= 2² × 3
18 = 2 × 3 × 3
= 2 × 3²
24 = 2 × 2 × 2 × 3
= 2³ × 3

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

PrimeIn 12In 18In 24Highest Power
22²2¹2³2³ = 8
33¹3²3¹3² = 9

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

LCM = 2³ × 3² = 8 × 9 = 72

Full Written Solution for the LCM of 12, 18, and 24

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(12, 18, 24) = 72:

Method A: Prime Factorization

  • • 12 = 2² × 3
  • • 18 = 2 × 3²
  • • 24 = 2³ × 3

Multiply the highest power of each prime: 2³ × 3² = 72.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 12, 18, and 24 is 6.

72 ÷ 12 = 6 (remainder 0 ✓)
72 ÷ 18 = 4 (remainder 0 ✓)
72 ÷ 24 = 3 (remainder 0 ✓)

Real-World & Fraction Context

Packaging boxes that hold 12, 18, or 24 items can all pack a 72-item master carton cleanly (6, 4, or 3 boxes per master carton).

Mistake to Watch Out For

Don't stop at 36 (36 is the LCM of 12 and 18, but 24 does not divide evenly into 36).