Skip to calculator
lcmcalculator.co

Worked Example • Consecutive Integers

LCM of 3 and 4 (Equals 12)

The Least Common Multiple of 3 and 4 is 12. Since 3 and 4 are neighboring whole numbers on the number line, they are coprime (GCF = 1), so their LCM is simply their product: 3 × 4 = 12.

2 to 10 integers • up to 18 digits each
Parsed:34
LCM of 3 and 4 Result
LCM(3, 4) = 12
Greatest Common Factor: GCF(3, 4) = 1No common factor greater than 1
Check the answer (every division leaves a remainder of 0):
12 ÷ 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.

3 = 3
= 3(prime)
4 = 2 × 2
= 2²

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

PrimeIn 3In 4Highest Power
2—2²2² = 4
33¹—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 3 and 4

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

Method A: Prime Factorization

  • • 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 3 and 4 is 1.

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

Real-World & Fraction Context

Adding 2/3 of an hour and 1/4 of an hour is effortless because a 60-minute clock is built around twelfths: 2/3 + 1/4 = 8/12 + 3/12 = 11/12 of an hour (55 minutes).

Mistake to Watch Out For

Don't confuse the prime factors of 4 (2 × 2) with 4 itself being prime. Even though 4 is composite, none of its prime factors (only 2s) match 3.