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Worked Example • Gold-Standard Textbook Pair

LCM of 12 and 18 (Equals 36)

The Least Common Multiple of 12 and 18 is 36. Because 12 (2² × 3¹) and 18 (2¹ × 3²) share a Greatest Common Factor of 6, their LCM is (12 × 18) ÷ 6 = 36.

2 to 10 integers • up to 18 digits each
Parsed:1218
LCM of 12 and 18 Result
LCM(12, 18) = 36
Greatest Common Factor: GCF(12, 18) = 6
Check the answer (every division leaves a remainder of 0):
36 ÷ 12 = 336 ÷ 18 = 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.

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

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

PrimeIn 12In 18Highest Power
22²2¹2² = 4
33¹3²3² = 9

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

LCM = 2² × 3² = 4 × 9 = 36

Full Written Solution for the LCM of 12 and 18

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(12, 18) = 36:

Method A: Prime Factorization

  • • 12 = 2² × 3
  • • 18 = 2 × 3²

Multiply the highest power of each prime: 2² × 3² = 36.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 12 and 18 is 6.

36 ÷ 12 = 3 (remainder 0 ✓)
36 ÷ 18 = 2 (remainder 0 ✓)

Real-World & Fraction Context

Two airport shuttles running on 12-minute and 18-minute loops meet at the terminal curb every 36 minutes (3 loops of the first shuttle, 2 loops of the second).

Mistake to Watch Out For

Adding the exponents (2³ × 3³ = 216) is the classic trap here—216 is 12 × 18, which fails to divide out the shared GCF of 6.