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Worked Example • Smallest Prime Pair

LCM of 2 and 3 (Equals 6)

The Least Common Multiple of 2 and 3 is 6. Because 2 is the only even prime number and 3 is the first odd prime number, they share no factors greater than 1, so you find their LCM by multiplying 2 × 3 = 6.

2 to 10 integers • up to 18 digits each
Parsed:23
LCM of 2 and 3 Result
LCM(2, 3) = 6
Greatest Common Factor: GCF(2, 3) = 1No common factor greater than 1
Check the answer (every division leaves a remainder of 0):
6 ÷ 2 = 36 ÷ 3 = 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.

2 = 2
= 2(prime)
3 = 3
= 3(prime)

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

PrimeIn 2In 3Highest Power
22¹—2¹ = 2
3—3¹3¹ = 3

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

LCM = 2¹ × 3¹ = 2 × 3 = 6

Full Written Solution for the LCM of 2 and 3

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(2, 3) = 6:

Method A: Prime Factorization

  • • 2 = 2
  • • 3 = 3

Multiply the highest power of each prime: 2¹ × 3¹ = 6.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 2 and 3 is 1.

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

Real-World & Fraction Context

When you add halves and thirds in kitchen measurements—such as 1/2 cup of butter plus 1/3 cup of sugar—you convert both fractions into sixths (3/6 + 2/6 = 5/6 cup) because 6 is the Least Common Denominator of 2 and 3.

Mistake to Watch Out For

Some beginners add 2 + 3 = 5 instead of multiplying. Remember that 5 is not divisible by either 2 or 3; the first number in both the 2-times table (2, 4, 6) and the 3-times table (3, 6) is 6.