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Worked Example • Introductory Triple

LCM of 2, 3, and 4 (Equals 12)

The Least Common Multiple of 2, 3, and 4 is 12. Even though GCF(2, 3, 4) = 1, the number 2 already divides evenly into 4, so the problem simplifies to LCM(3, 4) = 12.

2 to 10 integers • up to 18 digits each
Parsed:234
LCM of 2, 3, and 4 Result
LCM(2, 3, 4) = 12
Greatest Common Factor: GCF(2, 3, 4) = 1No common factor greater than 1
Check the answer (every division leaves a remainder of 0):
12 ÷ 2 = 612 ÷ 3 = 412 ÷ 4 = 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.

2 = 2
= 2(prime)
3 = 3
= 3(prime)
4 = 2 × 2
= 2²

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

PrimeIn 2In 3In 4Highest Power
22¹—2²2² = 4
3—3¹—3¹ = 3

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

LCM = 2² × 3¹ = 4 × 3 = 12

Full Written Solution for the LCM of 2, 3, and 4

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(2, 3, 4) = 12:

Method A: Prime Factorization

  • • 2 = 2
  • • 3 = 3
  • • 4 = 2²

Multiply the highest power of each prime: 2² × 3¹ = 12.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 2, 3, and 4 is 1.

12 ÷ 2 = 6 (remainder 0 ✓)
12 ÷ 3 = 4 (remainder 0 ✓)
12 ÷ 4 = 3 (remainder 0 ✓)

Real-World & Fraction Context

Adding 1/2 + 1/3 + 1/4 uses LCD(2, 3, 4) = 12: 6/12 + 4/12 + 3/12 = 13/12.

Mistake to Watch Out For

Don't multiply 2 × 3 × 4 = 24. Check if 12 is divisible by 2, 3, and 4—it is!